NUMERICAL METHOD FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR THE PARABOLIC EQUATION
https://doi.org/10.55452/1998-6688-2024-21-3-165-175
Abstract
A linear boundary value problem for a parabolic equation is considered in a closed domain. Based on the broken line method, the boundary value problem for a parabolic equation is replaced by a two-point boundary value problem for a system of linear ordinary differential equations by discretizing the unknown function u(t,x) with respect to the variable x. The obtained two-point boundary value problem is investigated by the parameterization method of Professor Dzhumabaev. Based on this method, an algorithm for finding a numerical solution to the two-point boundary value problem for a system of linear ordinary differential equations is constructed. The constructed algorithm is realized by applying known numerical methods. The constructiveness and efficiency of the parameterization method also allows us to construct a numerical solution of the considered linear boundary value problem for the parabolic equation. One numerical example is given to verify and illustrate the proposed algorithm.
About the Authors
N. B. Iskakova
Institute of Mathematics and Mathematical Modeling;
Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
Candidate of Phys.-Math.Sc., Leading Researcher
050010, Almaty;
050040, Almaty
Zh. М. Kadirbayeva
Institute of Mathematics and Mathematical Modeling;
Kazakh National Women's Teacher Training University;
International Information Technology University
Kazakhstan
Kazakhstan
Candidate of Phys.-Math.Sc., Leading Researcher
050010, Almaty;
050000, Almaty;
050000, Almaty
E. А. Bakirova
Institute of Mathematics and Mathematical Modeling;
Kazakh National Women's Teacher Training University;
Kazakhstan
Kazakhstan
Candidate of Phys.-Math.Sc., Leading Researcher
050010, Almaty;
050000, Almaty;
S. K. Kuanysh
Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
Doctoral student, Teacher
050040, Almaty
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Review
For citations:
Iskakova N.B., Kadirbayeva Zh.М., Bakirova E.А., Kuanysh S.K. NUMERICAL METHOD FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR THE PARABOLIC EQUATION. Herald of the Kazakh-British technical university. 2024;21(3):165-175. (In Kazakh) https://doi.org/10.55452/1998-6688-2024-21-3-165-175
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