Finite-difference methods for solving a nonlocal boundary value problem for a multidimensional parabolic equation with boundary conditions of integral form

DOI10.47910/FEMJ202201zbMath1500.65038MaRDI QIDQ5039323

Z. V. Beshtokova

Publication date: 12 October 2022

Published in: Dal'nevostochnyi Matematicheskii Zhurnal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/dvmg464

zbMATH Keywords

stabilityconvergenceparabolic equationdifference schemesa priori estimatenonlocal conditionmultidimensional problemlocally one-dimensional scheme

Mathematics Subject Classification ID

Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Second-order parabolic equations (35K10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Locally one-dimensional difference scheme for a nonlocal boundary value problem for a parabolic equation in a multidimensional domain
• On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Difference Methods of the Solution of Local and Non-local Boundary Value Problems for Loaded Equation of Thermal Conductivity of Fractional Order
• Nonlocal boundary value problems for a fractional-order convection-diffusion equation
• On an economical difference method for the solution of a multidimensional parabolic equation in an arbitrary region
• Об одной нелокальной задаче для уравнения теплопроводности с интегральным условием
• Difference schemes with a “disintegrating” operator for multidimensional problems
• The \(L_2\) solvability of a nonlocal problem with integral conditions for a hyperbolic equation
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