scholarly journals Fractional order convergence rate estimate of finite-difference method for the heat equation with concentrated capacity

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 331-338
Author(s):  
Bratislav Sredojevic ◽  
Dejan Bojovic
Keyword(s):  
Convergence Rate ◽  
Heat Equation ◽  
Fractional Order ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Order Convergence ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Sobolev Norms ◽  
Initial Boundary Value

The convergence of difference scheme for initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficient of the space derivatives, is considered. Fractional order convergence rate estimate in a special discrete Sobolev norms, compatible with the smoothness of the coefficient and solution, is proved.

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.

Fractional Order Convergence Rate Estimates Of Finite Difference Method On Nonuniform Meshes

2001 ◽  
Vol 1 (3) ◽  
pp. 213-221 ◽  
Author(s):  
Dejan Bojović ◽  
Boško Jovanović
Keyword(s):  
Finite Difference ◽  
Convergence Rate ◽  
Fractional Order ◽  
Finite Difference Schemes ◽  
Order Convergence ◽  
Interpolation Theory ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
The Poisson Equation ◽  
Nonuniform Meshes

AbstractIn this paper we show how the theory of interpolation of function spaces can be used to establish convergence rate estimates for finite difference schemes on nonuniform meshes. As a model problem we consider the first boundary value problem for the Poisson equation. Using the interpolation theory we construct a fractional-order convergence rate estimate which is consistent with the smoothness of data.

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 Finite difference approximation for the 2D heat equation with concentrated capacity

Filomat ◽  
2018 ◽  
Vol 32 (20) ◽  
pp. 6979-6987
Author(s):  
Bratislav Sredojevic ◽  
Dejan Bojovic
Keyword(s):  
Finite Difference ◽  
Heat Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Dependent ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Two Dimensional ◽  
Sobolev Norms ◽  
Initial Boundary Value

The convergence of difference scheme for two-dimensional initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficients of the space derivatives, is considered. An estimate of the rate of convergence in a special discrete Sobolev norms , compatible with the smoothness of the coefficients and solution, is proved.

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 Homotopy Analysis Method for a Fractional Order Equation with Dirichlet and Non-Local Integral Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1167
Author(s):  
Said Mesloub ◽  
Saleem Obaidat
Keyword(s):  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Initial Boundary Value

The main purpose of this paper is to obtain some numerical results via the homotopy analysis method for an initial-boundary value problem for a fractional order diffusion equation with a non-local constraint of integral type. Some examples are provided to illustrate the efficiency of the homotopy analysis method (HAM) in solving non-local time-fractional order initial-boundary value problems. We also give some improvements for the proof of the existence and uniqueness of the solution in a fractional Sobolev space.

Initial-boundary value problem for a fractional type degenerate heat equation

2018 ◽  
Vol 28 (06) ◽  
pp. 1199-1231
Author(s):  
Gerardo Huaroto ◽  
Wladimir Neves
Keyword(s):  
Heat Equation ◽  
Fractional Laplacian ◽  
Dirichlet Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Diffusion ◽  
Laplacian Operator ◽  
Initial Boundary Value ◽  
Fractional Laplacian Operator ◽  
Fractional Type

In this paper, we study a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the [Formula: see text]-fractional Laplacian operator, and the solvability is proved for any [Formula: see text].

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