DOI: https://doi.org/10.26089/NumMet.v23r210

Numerical method for solving a nonlocal boundary value problem for a multidimensional parabolic equation

Authors

  • Zaryana V. Beshtokova

Keywords:

nonlocal boundary value problems
a priori estimate
parabolic type equation
difference schemes
stability and convergence of difference schemes

Abstract

The work is devoted to nonlocal boundary value problems for a multidimensional parabolic equation with variable coefficients. The method of energy inequalities is used to obtain a priori estimates in differential and difference interpretations for solutions of nonlocal boundary value problems. The obtained estimates imply the uniqueness and stability of the solution of each of the considered problems with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem in the \(L_2\)-norm at a rate of \(O(|h|+\tau)\). For each of the considered problems, a numerical solution algorithm is constructed, and numerical calculations of test examples are carried out.

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Published

2022-06-12

Issue

Vol. 23 (2022): Issue 2.

Section

Methods and algorithms of computational mathematics and their applications

Author Biography

Zaryana V. Beshtokova

Institute of Applied Mathematics and Automation KBSC RAS
• Junior Researcherr

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