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Partial Differential Equations Commons

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All Articles in Partial Differential Equations

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810 full-text articles. Page 33 of 33.

The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh 2010 Imam Khomeini International University

The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the variational iteration method is applied for finding the solution of an Integro-differential parabolic problem with integral conditions. Convergence of the proposed method is also discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method.


An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta 2010 Banaras Hindu University

An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.


Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski 2010 Universite Pierre et Marie Curie

Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski

Publications

As a preliminary study to more complex situations of interest in small-scale technology, this paper envisages the elementary propagation properties of elastic waves in one-spatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure space-like and time-like material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on …


Comparison Differential Transformation Technique With Adomian Decomposition Method For Dispersive Long-Wave Equations In (2+1)-Dimensions, M. A. Mohamed 2010 Suez Canal University

Comparison Differential Transformation Technique With Adomian Decomposition Method For Dispersive Long-Wave Equations In (2+1)-Dimensions, M. A. Mohamed

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we will introduce two methods to obtain the numerical solutions for the system of dispersive long-wave equations (DLWE) in (2+1)-dimensions. The first method is the differential transformation method (DTM) and the second method is Adomian decomposition method (ADM). Moreover, we will make comparison between the solutions obtained by the two methods. Consequently, the results of our system tell us the two methods can be alternative ways for solution of the linear and nonlinear higher-order initial value problems.


Developing An Improved Shift-And-Invert Arnoldi Method, H. Saberi Najafi, M. Shams Solary 2010 Guilan University

Developing An Improved Shift-And-Invert Arnoldi Method, H. Saberi Najafi, M. Shams Solary

Applications and Applied Mathematics: An International Journal (AAM)

An algorithm has been developed for finding a number of eigenvalues close to a given shift and in interval [ Lb,Ub ] of a large unsymmetric matrix pair. The algorithm is based on the shift-andinvert Arnoldi with a block matrix method. The block matrix method is simple and it uses for obtaining the inverse matrix. This algorithm also accelerates the shift-and-invert Arnoldi Algorithm by selecting a suitable shift. We call this algorithm Block Shift-and-Invert or BSI. Numerical examples are presented and a comparison has been shown with the results obtained by Sptarn Algorithm in Matlab. The results show that the …


Improved Dust Acoustic Solitary Waves In Two Temperature Dust Fluids, E. K. El-Shewy, H. G. Abdelwahed, M. I. Abo el Maaty, M. A. Elmessary 2010 Mansoura University

Improved Dust Acoustic Solitary Waves In Two Temperature Dust Fluids, E. K. El-Shewy, H. G. Abdelwahed, M. I. Abo El Maaty, M. A. Elmessary

Applications and Applied Mathematics: An International Journal (AAM)

A theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear dust-acoustic solitary waves (DASWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Bolltzmannian ions and electrons. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge …


Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan 2010 Jordan University of Science and Technology

Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, He’s Variational iteration method (VIM) is used for the solution of singularly perturbed two-point boundary value problems with two small parameters multiplying the derivatives. Some problems are solved to demonstrate the applicability of the method. This paper suggests a patern for choosing the freely selected initial approximation in the VIM that leads to a very well approximation by only one iteration.


Inverse Heat Conduction Problem In A Semi-Infinite Circular Plate And Its Thermal Deflection By Quasi-Static Approach, K. C. Deshmukh, S. C. Warbhe, G. D. Kedar, V. S. Kulkarni 2010 Nagpur University

Inverse Heat Conduction Problem In A Semi-Infinite Circular Plate And Its Thermal Deflection By Quasi-Static Approach, K. C. Deshmukh, S. C. Warbhe, G. D. Kedar, V. S. Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

This paper concerns the inverse heat conduction problem in a semi-infinite thin circular plate subjected to an arbitrary known temperature under unsteady condition and the behavior of thermal deflection has been discussed on the outer curved surface with the help of mathematical modeling. The solutions are obtained in an analytical form by using the integral transform technique.


Soliton And Periodic Solutions For (3+1)-Dimensional Nonlinear Evolution Equations By Exp-Function Method, A. Borhanifar, M. M. Kabir 2010 University of Mohaghegh Ardabili

Soliton And Periodic Solutions For (3+1)-Dimensional Nonlinear Evolution Equations By Exp-Function Method, A. Borhanifar, M. M. Kabir

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, (3+1)-dimensional Jimbo-Miwa and (3+1)-dimensional potential-YTSF equations are considered and the Exp-Function method is employed to compute the exact solutions. The solutions obtained by this method are compared with the exact solutions obtained through other methods. These equations play a very important role in mathematical physics and engineering sciences. It is shown that the Exp-Function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics


High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis 2010 California Polytechnic State University, San Luis Obispo

High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis

Master's Theses

A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0 and sub-zonal pressure Q1-Q1d. Several test problems are considered including static convergence …


Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner 2010 Western Kentucky University

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mathematics Faculty Publications

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational presentation for senior physics majors


Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner 2010 Western Kentucky University

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mathematics Faculty Publications

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational/Research presentation for senior physics majors


The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov 2010 Technological University Dublin

The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov

Conference papers

The theory of soliton perturbations is considered. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton solution one can ’modify’ …


Two Soliton Interactions Of Bd.I Multicomponent Nls Equations And Their Gauge Equivalent, Vladimir Gerdjikov, Georgi Grahovski 2010 Bulgarian Academy of Sciences

Two Soliton Interactions Of Bd.I Multicomponent Nls Equations And Their Gauge Equivalent, Vladimir Gerdjikov, Georgi Grahovski

Conference papers

Using the dressing Zakharov-Shabat method we re-derive the effects of the two-soliton interactions for the MNLS equations related to the BD.I-type symmetric spaces. Next we generalize this analysis for the Heisenberg ferromagnet type equations, gauge equivalent to MNLS.


Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev 2010 Institute of Continuous Media Mechanics

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O Bi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.


Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev 2010 Western Kentucky University

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O Bi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.


Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, Vladimir Gerdjikov, Georgi Grahovski 2010 Bulgarian Academy of Sciences

Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, Vladimir Gerdjikov, Georgi Grahovski

Articles

The algebraic structure and the spectral properties of a special class of multicomponent NLS equations, related to the symmetric spaces of BD.I-type are analyzed. The focus of the study is on the spectral theory of the associated Lax operator to these nonlinear evolutionary equations for different fundamental representations of the underlying simple Lie algebra g. Special attention is paid to the spinor representation of the orthogonal Lie algebras of B type.


Parallel And Distributed Simulation Of Parabolic And Telegraphic Equations., Ewedafe Simon Uzezi 2010 Universiti Malaya

Parallel And Distributed Simulation Of Parabolic And Telegraphic Equations., Ewedafe Simon Uzezi

Student Works (2010-2019)

In this thesis, a parallel implementation of explicit/implicit parallel algorithms such as the stationary iterative methods and the class of iterating alternating methods which includes: Alternating Direction Implicit (ADI), Iterative Alternating Direction Explicit (IADE), for D’Yakonov (IADE-DY), Double sweep Mitchell and Fairweather (MF-DS) and Alternating Group Explicit (AGE) method for solving 1-Dimensional (1-D), 2-Dimensional (2-D) Parabolic (special examples including 1-D, 2-D Bio-Heat Equation) and 1-D, 2-D and 3-D Telegraphic Equations on a distributed environment of Message Passing Interface (MPI) and Parallel Virtual Machine (PVM) platform is presented. To correlate the communication activity with computation, we counted events between significant MPI/PVM …


Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht 2010 Tallinn University of Technology

Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht

Publications

Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model.


Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski 2010 Tallinn University of Technology

Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski

Publications

The basic time scales for current-induced net transport of surface water and associated time scales of reaching the nearshore in the Gulf of Finland, the Baltic Sea, are analysed based on Lagrangian trajectories of water particles reconstructed from three-dimensional velocity fields by the Rossby Centre circulation model for 1987–1991. The number of particles reaching the nearshore exhibits substantial temporal variability whereas the rate of leaving the gulf is almost steady. It is recommended to use an about 3 grid cells wide nearshore area as a substitute to the coastal zone and about 10–15 day long trajectories for calculations of the …


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