Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Mathematics Faculty Publications

Discipline
Institution
Keyword
Publication Year
File Type

Articles 91 - 120 of 562

Full-Text Articles in Mathematics

Concerning A Decision-Diagram-Based Solution To The Generalized Directed Rural Postman Problem, Renzo Roel P. Tan, Jun Kawahara, Kazushi Ikeda, Agnes Garciano, Kyle Stephen S. See Jun 2020

Concerning A Decision-Diagram-Based Solution To The Generalized Directed Rural Postman Problem, Renzo Roel P. Tan, Jun Kawahara, Kazushi Ikeda, Agnes Garciano, Kyle Stephen S. See

Mathematics Faculty Publications

Decision-diagram-based solutions for discrete optimization have been persistently studied. Among these is the use of the zero-suppressed binary decision diagram, a compact graph-based representation for a specified family of sets. Such a diagram may work out combinatorial problems by efficient enumeration. In brief, an extension to the frontierbased search approach for zero-suppressed binary decision diagram construction is proposed. The modification allows for the inclusion of a class-determined constraint in formulation. Variations of the generalized directed rural postman problem, proven to be nondeterministic polynomial-time hard, are solved on some rapid transit systems as illustration. Lastly, results are juxtaposed against standard integer …

Go to article

Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr. Mar 2020

Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr.

Mathematics Faculty Publications

Underwater Gesture Recognition is a challenging task since conditions which are normally not an issue in gesture recognition on land must be considered. Such issues include low visibility, low contrast, and unequal spectral propagation. In this work, we explore the underwater gesture recognition problem by taking on the recently released Cognitive Autonomous Diving Buddy Underwater Gestures dataset. The contributions of this paper are as follows: (1) Use traditional computer vision techniques along with classical machine learning to perform gesture recognition on the CADDY dataset; (2) Apply deep learning using a convolutional neural network to solve the same problem; (3) Perform …

Go to article

Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas Feb 2020

Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas

Mathematics Faculty Publications

A geometric realization of an abstract polyhedron P is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Gamma. The method entails finding a real orthogonal representation of Gamma of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.

Go to article

Boolean Network Topologies And The Determinative Power Of Nodes, Bronson W. Wacker, Mihaela T. Velcsov, Jim A. Rogers Feb 2020

Boolean Network Topologies And The Determinative Power Of Nodes, Bronson W. Wacker, Mihaela T. Velcsov, Jim A. Rogers

Mathematics Faculty Publications

Boolean networks have been used extensively for modeling networks whose node activity could be simplified to a binary outcome, such as on-off. Each node is influenced by the states of the other nodes via a logical Boolean function. The network is described by its topological properties which refer to the links between nodes, and its dynamical properties which refer to the way each node uses the information obtained from other nodes to update its state. This work explores the correlation between the information stored in the Boolean functions for each node in a property known as the determinative power and …

Go to article

Approximate And Exact Merging Of Knapsack Constraints With Cover Inequalities, Fabio Vitor, Todd Easton Jan 2020

Approximate And Exact Merging Of Knapsack Constraints With Cover Inequalities, Fabio Vitor, Todd Easton

Mathematics Faculty Publications

This paper presents both approximate and exact merged knapsack cover inequalities, a class of cutting planes for knapsack and multiple knapsack integer programs. These inequalities combine the information from knapsack constraints and cover inequalities. Approximate merged knapsack cover inequalities can be generated through a O(n log n) algorithm, where n is the number of variables. This class of inequalities can be strengthened to an exact version with a pseudo-polynomial time algorithm. Computational experiments demonstrate an average improvement of approximately 8% in solution time and 5% in the number of ticks from CPLEX when approximate merged knapsack cover …

Go to article

On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino Jan 2020

On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino

Mathematics Faculty Publications

A vertex coloring c : V(G) → of a non-trivial connected graph G is called a set coloring if NC(u) ≠ NC(v) for any pair of adjacent vertices u and v. Here, NC(x) denotes the set of colors assigned to vertices adjacent to x. The set chromatic number of G, denoted by χs (G), is defined as the fewest number of colors needed to construct a set coloring of G. In this paper, we study the set chromatic number in relation to two graph operations: …

Go to article

Sigma Chromatic Number Of Graph Coronas Involving Complete Graphs, Agnes Garciano, Maria Czarina T. Lagura, Reginaldo M. Marcelo Jan 2020

Sigma Chromatic Number Of Graph Coronas Involving Complete Graphs, Agnes Garciano, Maria Czarina T. Lagura, Reginaldo M. Marcelo

Mathematics Faculty Publications

Let c : V(G) → be a coloring of the vertices in a graph G. For a vertex u in G, the color sum of u, denoted by σ(u), is the sum of the colors of the neighbors of u. The coloring c is called a sigma coloring of G if σ(u) ≠ σ(v) whenever u and v are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic …

Go to article

The N-Integral, Abraham P. Racca, Emmanuel A. Cabral Jan 2020

The N-Integral, Abraham P. Racca, Emmanuel A. Cabral

Mathematics Faculty Publications

In this paper, we introduced a Henstock-type integral named $N$-integral of a real valued function $f$ on a closed and bounded interval $[a,b]$. The $N$-integrable functions lie entirely between Riemann integrable functions and Henstock integrable functions. It was shown that for a Henstock integrable function $f$ on $[a,b]$ the following are equivalent: \begin{enumerate} \item[$(1)$] The function $f$ is $N$-integrable; \item[$(2)$] There exists a null set $S$ for which given $\epsilon >0$ there exists a gauge $\delta$ such that for any $\delta$-fine partial division $D=\{(\xi,[u,v])\}$ of $[a,b]$ we have \[(\phi_S(D)\cap \Gamma_{\epsilon})\sum |f(v)-f(u)||v-u|<\epsilon\] where $\phi_S(D)=\{(\xi,[u,v])\in D:\xi \notin S\}$ and \[\Gamma_{\epsilon}=\{(\xi,[u,v]): |f(v)-f(u)|\geq \epsilon\}\] \end{enumerate} and \begin{enumerate} \item[$(3)$] The function $f$ is continuous almost everywhere. \end{enumerate} A characterization of continuous almost everywhere functions was also given.

Go to article

Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza Jan 2020

Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza

Mathematics Faculty Publications

Developing countries typically do not perform well in international benchmarks of mathematics achievement. This may be partially explained by students’ immersion in classrooms characterized by superficial strategies or rote-learning methods. This paper reports on the design of mobile applications (apps) developed by the authors as part of an ongoing project funded by a national government agency and intended to promote structural thinking and statistical reasoning. It describes the general features of the apps, as well as the pedagogical principles upon which the apps’ designs were anchored on. These principles are grounded on research and established practices on number sense and …

Go to article

Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman Jan 2020

Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman

Mathematics Faculty Publications

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …

Go to article

Three Point Boundary Value Problems For Ordinary Differential Equations, Uniqueness Implies Existence, Paul W. Eloe, Johnny Henderson, Jeffrey T. Neugebauer Jan 2020

Three Point Boundary Value Problems For Ordinary Differential Equations, Uniqueness Implies Existence, Paul W. Eloe, Johnny Henderson, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We consider a family of three point n − 2, 1, 1 conjugate boundary value problems for nth order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of n−point boundary value problems. Here, we replace that standard hypothesis with one in which we assume uniqueness of solutions of large families of two and three point boundary value problems. We then close the paper with verifiable conditions on the …

Go to article

Free Subgroups With Torsion Quotients And Profinite Subgroups With Torus Quotients, Wayne Lewis, Peter Loth, Adolf Mader Jan 2020

Free Subgroups With Torsion Quotients And Profinite Subgroups With Torus Quotients, Wayne Lewis, Peter Loth, Adolf Mader

Mathematics Faculty Publications

Here “group” means abelian group. Compact connected groups contain δ-subgroups, that is, compact totally disconnected subgroups with torus quotients, which are essential ingredients in the important Resolution Theorem, a description of compact groups. Dually, full free subgroups of discrete torsion-free groups of finite rank are studied in order to obtain a comprehensive picture of the abundance of δ-subgroups of a protorus. Associated concepts are also considered.

Go to article

The Sigma Chromatic Number Of The Sierpinski Gasket Graphs And The Hanoi Graphs, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino Jan 2020

The Sigma Chromatic Number Of The Sierpinski Gasket Graphs And The Hanoi Graphs, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino

Mathematics Faculty Publications

A vertex coloring c : V(G) → of a non-trivial connected graph G is called a sigma coloring if σ(u) ≠ σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we determine the sigma chromatic numbers of the …

Go to article

Twin Chromatic Indices Of Some Graphs With Maximum Degree 3, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino Jan 2020

Twin Chromatic Indices Of Some Graphs With Maximum Degree 3, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in k ) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by . In this paper, we determine the …

Go to article

On Eigenvalue Bounds For The Finite-State Birth-Death Process Intensity Matrix, R.R.P Tan, K Ikeda, Len Patrick Dominic M. Garces Jan 2020

On Eigenvalue Bounds For The Finite-State Birth-Death Process Intensity Matrix, R.R.P Tan, K Ikeda, Len Patrick Dominic M. Garces

Mathematics Faculty Publications

The paper sets forth a novel eigenvalue interlacing property across the finite-state birth-death process intensity matrix and two clearly identified submatrices as an extension of Cauchy’s interlace theorem for Hermitian matrix eigenvalues. A supplemental proof involving an examination of probabilities acquired from specific movements across states and a derivation of a form for the eigenpolynomial of the matrix through convolution and Laplace transform is then presented towards uncovering a similar characteristic for the general Markov chain transition rate matrix. Consequently, the proposition generates bounds for each eigenvalue of the original matrix, easing numerical computation. To conclude, the applicability of the …

Go to article

Digital Simulations For Grade 7 To 10 Mathematics, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Verzosa, Maria Alva Q. Aberin, Len Patrick Dominic M. Garces, Flordeliza F. Francisco, Evangeline P. Bautista, Mark Anthony C. Tolentino, Winfer C. Tabares Dec 2019

Digital Simulations For Grade 7 To 10 Mathematics, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Verzosa, Maria Alva Q. Aberin, Len Patrick Dominic M. Garces, Flordeliza F. Francisco, Evangeline P. Bautista, Mark Anthony C. Tolentino, Winfer C. Tabares

Mathematics Faculty Publications

This article describes a Department of Science and Technology – Philippine Council for Industry, Energy and Emerging Technology (DOST-PCIEERD) project aimed to facilitate the implementation of the mathematical objectives raised by the Department of Education’s (DepEd) K to 12 program in the Philippines through the use of innovative digital technologies. In particular, a selection of application software (“apps”) were created for Grade 7 to 10 mathematics that covered topics indicated in the five strands outlined in the K to 12 program – namely (1) number, (2) geometry, (3) measurement, (4) patterns and algebra, and (5) statistics and probability. The design …

Go to article

A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin Nov 2019

A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin

Mathematics Faculty Publications

We prove a generalization of Schroter's formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the well-known identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist's Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q)(infinity) and (q; q)(infinity)(k), k >= 3, as combinations of Jacobi triple products, are also proved.

Go to article

Quasilinearization And Boundary Value Problems At Resonance, Kareem Alanazi, Meshal Alshammari, Paul W. Eloe Oct 2019

Quasilinearization And Boundary Value Problems At Resonance, Kareem Alanazi, Meshal Alshammari, Paul W. Eloe

Mathematics Faculty Publications

A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

Go to article

Local And Global Color Symmetries Of A Symmetrical Pattern, Ma. Louise Antonette N. De Las Peñas, Agatha Kristel Abila, Eduard C. Taganap Aug 2019

Local And Global Color Symmetries Of A Symmetrical Pattern, Ma. Louise Antonette N. De Las Peñas, Agatha Kristel Abila, Eduard C. Taganap

Mathematics Faculty Publications

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern P consisting of disjoint congruent symmetric motifs. The pattern P has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of P ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of P, a coloring that is perfect and transitive under G, satisfying the condition that the coloring …

Go to article

Two Dimensional Search Algorithms For Linear Programming, Fabio Torres Vitor Aug 2019

Two Dimensional Search Algorithms For Linear Programming, Fabio Torres Vitor

Mathematics Faculty Publications

Linear programming is one of the most important classes of optimization problems. These mathematical models have been used by academics and practitioners to solve numerous real world applications. Quickly solving linear programs impacts decision makers from both the public and private sectors. Substantial research has been performed to solve this class of problems faster, and the vast majority of the solution techniques can be categorized as one dimensional search algorithms. That is, these methods successively move from one solution to another solution by solving a one dimensional subspace linear program at each iteration. This dissertation proposes novel algorithms that move …

Go to article

Mittag–Leffler Stability Of Systems Of Fractional Nabla Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda Jul 2019

Mittag–Leffler Stability Of Systems Of Fractional Nabla Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

Go to article

A Zero-Suppressed Binary Decision Diagram Approach For Constrained Path Enumeration, Renzo Roel P. Tan, Jun Kawahara, Agnes Garciano, Immanuel Sin Jul 2019

A Zero-Suppressed Binary Decision Diagram Approach For Constrained Path Enumeration, Renzo Roel P. Tan, Jun Kawahara, Agnes Garciano, Immanuel Sin

Mathematics Faculty Publications

Combinatorial optimization over graphs has been the subject of research. Recently, the solution of such problems by enumeration using a compact data structure called the zero-suppressed binary decision diagram was proposed and studied. The paper augments the existing frontier-based search method of construction and puts forth a technique for accommodating additional constraints during computation. The shortest and longest path problems for the Osaka Metro transit network are simultaneously solved as demonstration. Furthermore, a comparison of the approach with a conventional integer programming method is presented towards justifying the effectiveness of the algorithm.

Go to article

Weighted Composition Operators On The Hilbert Hardy Space Of A Half-Plane, Valentin Matache May 2019

Weighted Composition Operators On The Hilbert Hardy Space Of A Half-Plane, Valentin Matache

Mathematics Faculty Publications

Operators of type f→ψf∘ϕ acting on function spaces are called weighted composition operators. If the weight function ψ is the constant function 1, then they are called composition operators. We consider weighted composition operators acting on the Hilbert Hardy space of a half-plane and study compactness, boundedness, invertibility, normality and spectral properties of such operators.

Go to article

Impartial Achievement Games For Generating Nilpotent Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben May 2019

Impartial Achievement Games For Generating Nilpotent Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Mathematics Faculty Publications

We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form T×H, where T is a 2-group and H is a group of odd order. This includes all nilpotent and hence abelian groups.

Go to article

Graceful Labeling Of Triangular Extension Of Complete Bipartite Graph, Sarbari Mitra, Soumya Bhoumik Jan 2019

Graceful Labeling Of Triangular Extension Of Complete Bipartite Graph, Sarbari Mitra, Soumya Bhoumik

Mathematics Faculty Publications

For positive integers m, n, K m,n represents the complete bipartite graph. We name the graph G = K m,n ⊙ K2 as triangular extension of complete bipartite graph K m,n , since there is a triangle hanging from every vertex of K m,n . In this paper we show that G is graceful when m = n = 2ℓ, for any integer ℓ.

Go to article

Bochner-Kähler And Bach Flat Manifolds, Amalendu Ghosh, Ramesh Sharma Jan 2019

Bochner-Kähler And Bach Flat Manifolds, Amalendu Ghosh, Ramesh Sharma

Mathematics Faculty Publications

We have classified Bochner-Kähler manifolds of real dimension > 4, which are also Bach flat. In the 4-dimensional case, we have shown that, if the scalar curvature is harmonic, then it is constant. Finally, we show that the gradient of scalar curvature of any Bochner-Kähler manifold is an infinitesimal harmonic transformation, and if it is conformal then the scalar curvature is constant.

Go to article

Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations, Paul W. Eloe, Catherine Kublik, Jeffrey T. Neugebauer Jan 2019

Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations, Paul W. Eloe, Catherine Kublik, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this paper, we obtain sign conditions and comparison theorems for Green's functions of a family of boundary value problems for a Riemann-Liouville type delta fractional difference equation. Moreover, we show that as the length of the domain diverges to infinity, each Green's function converges to a uniquely defined Green's function of a singular boundary value problem.

Go to article

L(2, 1)-Labeling Of Circulant Graphs, Sarbari Mitra, Soumya Bhoumik Jan 2019

L(2, 1)-Labeling Of Circulant Graphs, Sarbari Mitra, Soumya Bhoumik

Mathematics Faculty Publications

An L(2, 1)-labeling of a graph Γ is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let λ12(Γ) denote the least λ such that Γ admits an L(2, 1)-labeling using labels from {0, 1, . . ., λ}. A Cayley graph of group G is called a circulant graph of order n, if G = Zn. In this paper initially we investigate the upper bound for the span of the L(2, 1)-labeling for …

Go to article

Quasilinearization And Boundary Value Problems At Resonance For Caputo Fractional Differential Equations, Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer Jan 2019

Quasilinearization And Boundary Value Problems At Resonance For Caputo Fractional Differential Equations, Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The quasilinearization method is applied to a boundary value problem at resonance for a Caputo fractional differential equation. The method of upper and lower solutions is first employed to obtain the uniqueness of solutions of the boundary value problem at resonance. The shift argument is applied to show the existence of solutions. The quasilinearization algorithm is then developed and sequences of approximate solutions are constructed that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two applications are provided to illustrate the main results.

Go to article

Analysis Of Optimal Superconvergence Of A Local Discontinuous Galerkin Method For Nonlinear Second-Order Two-Point Boundary-Value Problems, Mahboub Baccouch Jan 2019

Analysis Of Optimal Superconvergence Of A Local Discontinuous Galerkin Method For Nonlinear Second-Order Two-Point Boundary-Value Problems, Mahboub Baccouch

Mathematics Faculty Publications

In this paper, we investigate the convergence and superconvergence properties of a local discontinuous Galerkin (LDG) method for nonlinear second-order two-point boundary-value problems (BVPs) of the form u″=f(x,u,u′), x∈[a,b] subject to some suitable boundary conditions at the endpoints x=a and x=b. We prove optimal L2 error estimates for the solution and for the auxiliary variable that approximates the first-order derivative. The order of convergence is proved to be p+1, when piecewise polynomials of degree at most p are used. We further prove that the derivatives of the LDG solutions are superconvergent with order p+1toward the derivatives of Gauss-Radau projections of …

Go to article

First Prev Next Last