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Articles 1 - 12 of 12
Full-Text Articles in Analysis
Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros
Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros
Mathematical Modelling and Numerical Simulation with Applications
This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and …
Data-Assimilation-Enabled Fast Convergence Of The Uzawa Scheme For Navier-Stokes Equations With Large Reynolds Numbers, Jessica C. Franklin
Data-Assimilation-Enabled Fast Convergence Of The Uzawa Scheme For Navier-Stokes Equations With Large Reynolds Numbers, Jessica C. Franklin
All Theses
This work studies efficient techniques utilized to solve the Navier-Stokes equations that model incompressible Newtonian flow in the setting where partial solution data is available. First, we analyze the Picard iteration and Picard with continuous data assimilation applied and test convergence. Then, we analyze the Arrow-Hurwicz (AH) and Uzawa iterative procedures and test convergence. Finally, we apply continuous data assimilation to Uzawa, and analytical and numerical results show that CDA improves Uzawa convergence for the NSE, similar to CDA-Picard but it is much more efficient.
Dream Series, Jim Wolper
Dream Series, Jim Wolper
Journal of Humanistic Mathematics
Dream Series converge to numbers we cannot analyze. They exist, like dreams, but resist attempts to put them into order.
(R1521) On Weighted Lacunary Interpolation, Swarnima Bahadur, Sariya Bano
(R1521) On Weighted Lacunary Interpolation, Swarnima Bahadur, Sariya Bano
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we considered the non-uniformly distributed zeros on the unit circle, which are obtained by projecting vertically the zeros of the derivative of Legendre polynomial together with x=1 and x=-1 onto the unit circle. We prescribed the function on the above said nodes, while its second derivative at all nodes except at x=1 and x=-1 with suitable weight function and obtained the existence, explicit forms and establish a convergence theorem for such interpolatory polynomial. We call such interpolation as weighted Lacunary interpolation on the unit circle.
Algebraic, Analytic, And Combinatorial Properties Of Power Product Expansions In Two Independent Variables., Mohamed Ammar Elewoday
Algebraic, Analytic, And Combinatorial Properties Of Power Product Expansions In Two Independent Variables., Mohamed Ammar Elewoday
Graduate Theses, Dissertations, and Problem Reports (ETD)
Let $F(x,y)=I+\hspace{-.3cm}\sum\limits_{\substack{p=1\\m+n=p}}^{\infty}\hspace{-.3cm}A_{m,n}x^my^n$ be a formal power series, where the coefficients $A_{m,n}$ are either all matrices or all scalars. We expand $F(x,y)$ into the formal products $\prod\limits_{\substack{p=1\\m+n=p}}^{\infty}\hspace{-.3cm}(I+G_{m,n}x^m y^n)$, $\prod\limits_{\substack{p=1\\m+n=p}}^{\infty}\hspace{-.3cm}(I-H_{m,n}x^m y^n)^{-1}$, namely the \textit{ power product expansion in two independent variables} and \textit{inverse power product expansion in two independent variables} respectively. By developing new machinery involving the majorizing infinite product, we provide estimates on the domain of absolute convergence of the infinite product via the Taylor series coefficients of $F(x,y)$. This machinery introduces a myriad of "mixed expansions", uncovers various algebraic connections between the $(A_{m,n})$ and the $(G_{m,n})$, and uncovers various algebraic …
Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri
Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples.
An Ishikawa-Type Iterative Algorithm For Solving A Generalized Variational Inclusion Problem Involving Difference Of Monotone Operators, Mohd Ishtyak, Rais Ahmad
An Ishikawa-Type Iterative Algorithm For Solving A Generalized Variational Inclusion Problem Involving Difference Of Monotone Operators, Mohd Ishtyak, Rais Ahmad
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study a generalized variational inclusion problem involving difference of monotone operators in Hilbert spaces. We established equivalence between the generalized variational inclusion problem and a fixed point problem. We establish an Ishikawa type iterative algorithm for solving a generalized variational inclusion problem involving difference of monotone operators, which is more general than Mann-type iterative algorithm. An existence result as well as a convergence result are proved separately. The problem of this paper is more general than many existing problems in the literature. Several special cases of generalized variational inclusion problem involving difference of monotone operators are …
Properties And Convergence Of State-Based Laplacians, Kelsey Wells
Properties And Convergence Of State-Based Laplacians, Kelsey Wells
Department of Mathematics: Dissertations, Theses, and Student Research
The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different …
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented.
Random Variational-Like Inclusion And Random Proximal Operator Equation For Random Fuzzy Mappings In Banach Spaces, Rais Ahmad, Iqbal Ahmad, Mijanur Rahaman
Random Variational-Like Inclusion And Random Proximal Operator Equation For Random Fuzzy Mappings In Banach Spaces, Rais Ahmad, Iqbal Ahmad, Mijanur Rahaman
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal operator equation for random fuzzy mappings. This equivalence is used to define an iterative algorithm for solving random proximal operator equation for random fuzzy mappings. Through an example, we show that the random Wardrop equilibrium problem is a special case of the random variational-like inclusion …
On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri
On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples.
The Fuzzy Over-Relaxed Proximal Point Iterative Scheme For Generalized Variational Inclusion With Fuzzy Mappings, Rais Ahmad, Mijanur Rahaman, Haider A. Rizvi
The Fuzzy Over-Relaxed Proximal Point Iterative Scheme For Generalized Variational Inclusion With Fuzzy Mappings, Rais Ahmad, Mijanur Rahaman, Haider A. Rizvi
Applications and Applied Mathematics: An International Journal (AAM)
This paper deals with the introduction of a fuzzy over-relaxed proximal point iterative scheme based on H(-, -)-cocoercivity framework for solving a generalized variational inclusion problem with fuzzy mappings. The resolvent operator technique is used to approximate the solution of generalized variational inclusion problem with fuzzy mappings and convergence of the iterative sequences generated by the iterative scheme is discussed. Our results can be treated as refinement of many previously-known results.