scholarly journals Additive difference scheme for two-dimensional fractional in time diffusion equation

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 217-226 ◽  
Author(s):  
Sandra Hodzic-Ivanovic ◽  
Bosko Jovanovic
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Numerical Approximation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensional ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

An additive finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional fractional in time diffusion equation is proposed. Its stability is investigated and a convergence rate estimate is obtained.

scholarly journals Factorized difference scheme for 2D fractional in time diffusion equation

2015 ◽  
Vol 9 (2) ◽  
pp. 199-208 ◽  
Author(s):  
Sandra Hodzic
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Numerical Approximation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensional ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

A factorized finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional fractional in time diffusion equation is proposed. Its stability is investigated and a convergence rate estimate is obtained.

scholarly journals Factorized difference scheme for two-dimensional subdiffusion equation in nonhomogeneous media

2016 ◽  
Vol 99 (113) ◽  
pp. 1-13 ◽  
Author(s):  
Aleksandra Delic ◽  
Sandra Hodzic ◽  
Bosko Jovanovic
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Approximation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Nonhomogeneous Media ◽  
Subdiffusion Equation ◽  
Initial Boundary Value

A factorized finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional subdiffusion equation in nonhomogeneous media is proposed. Its stability and convergence are investigated. The corresponding error bounds are obtained.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

scholarly journals Conservative Linear Difference Scheme for Rosenau-KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinsong Hu ◽  
Youcai Xu ◽  
Bing Hu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Kdv Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
The Difference ◽  
Second Order Convergence ◽  
Initial Boundary Value ◽  
Theoretical Results

A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed. The difference scheme simulates two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

scholarly journals An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Maobo Zheng ◽  
Jun Zhou
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Kdv Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Discrete Energy ◽  
The Difference ◽  
Initial Boundary Value ◽  
Theoretical Results

An average linear finite difference scheme for the numerical solution of the initial-boundary value problem of Generalized Rosenau-KdV equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy norm method. It is shown that the finite difference scheme is 2nd-order convergent and unconditionally stable. Numerical experiments verify that the theoretical results are right and the numerical method is efficient and reliable.

scholarly journals A linear finite difference scheme for the generalized dissipative symetric regularized long wave equation with damping

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 719-726 ◽  
Author(s):  
Xi Wang ◽  
Jin-Song Hu ◽  
Hong Zhang
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Initial Boundary Value

In this paper, we study and analyze a three-level linear finite difference scheme for the initial boundary value problem of the symmetric regularized long wave equation with damping. The proposed scheme has the second accuracy both for the spatial and temporal discretization. The convergence and stability of the numerical solutions are proved by the mathematical induction and the discrete functional analysis. Numerical results are given to verify the accuracy and the efficiency of proposed algorithm.

scholarly journals PRACTICAL ERROR ANALYSIS FOR THE THREE-LEVEL BILINEAR FEM AND FINITE-DIFFERENCE SCHEME FOR THE 1D WAVE EQUATION WITH NON-SMOOTH DATA

2018 ◽  
Vol 23 (3) ◽  
pp. 359-378
Author(s):  
Alexander Zlotnik ◽  
Olga Kireeva
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Error Analysis ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Free Term ◽  
The Rich ◽  
Initial Boundary Value

We deal with the standard three-level bilinear FEM and finite-difference scheme with a weight to solve the initial-boundary value problem for the 1D wave equation. We consider the rich collection of initial data and the free term which are the Dirac δ-functions, discontinuous, continuous but with discontinuous derivatives and from the Sobolev spaces, accomplish the practical error analysis in the L2, L1, energy and uniform norms as the mesh re_nes and compare results with known theoretical error bounds.

scholarly journals Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation

2003 ◽  
Vol 2003 (16) ◽  
pp. 899-922 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Diffusion Equation ◽  
Integral Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensional ◽  
Dimensional Diffusion ◽  
Rothe Method ◽  
Semidiscrete Approximation ◽  
Initial Boundary Value ◽  
The Given

This paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by means of the Rothe method. Besides, convergence and an error estimate for a semidiscrete approximation are obtained.

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