Parabolic equation with periodic condition on the so¬lution and the projection-difference method of its approximate solution

10.12737/5116 ◽  
2014 ◽  
Vol 2 (4) ◽  
pp. 69-72
Author(s):  
A. Bondarev
Keyword(s):  
Approximate Solution ◽  
Parabolic Equation ◽  
Difference Method ◽  
Periodic Condition

THE STRONG-NORM CONVERGENCE OF A PROJECTION-DIFFERENCE METHOD OF SOLUTION OF A PARABOLIC EQUATION WITH THE PERIODIC CONDITION ON THE SOLUTION

2018 ◽  
pp. 617-623
Author(s):  
Andrei Sergeevich Bondarev
Keyword(s):  
Exact Solution ◽  
Parabolic Equation ◽  
Difference Method ◽  
Approximate Solutions ◽  
Linear Parabolic Equation ◽  
Periodic Condition ◽  
Method Of Solution ◽  
The Galerkin Method ◽  
Convergence Of Approximate Solutions ◽  
Strong Norm

A smooth soluble abstract linear parabolic equation with the periodic condition on the solution is treated in a separable Hilbert space. This problem is solved approximately by a projection-difference method using the Galerkin method in space and the implicit Euler scheme in time. Effective both in time and in space strong-norm error estimates for approximate solutions, which imply convergence of approximate solutions to the exact solution and order of convergence rate depending of the smoothness of the exact solution, are obtained.

Research on the Forward Euler Difference Method for Parabolic Equations

2014 ◽  
Vol 998-999 ◽  
pp. 992-995
Author(s):  
You Guo Li ◽  
Yuan Fei Dong
Keyword(s):  
Parabolic Equation ◽  
Numerical Experiment ◽  
Difference Scheme ◽  
Difference Method ◽  
Parabolic Equations ◽  
Convergence And Stability ◽  
Forward Euler ◽  
Theoretical Results

This article is devoted to the forward Euler difference method for the parabolic equation. In this paper, a forward Euler difference scheme is derived. It is shown that the forward Euler difference scheme is convergence and stability. Moreover, a numerical experiment is conducted to illustrate the theoretical results of the presented method.

Sign in / Sign up

Export Citation Format

Share Document