The Numerical Implementation of the Linear IntegroDifferential Equations Method for the Solution of Non-Stationary Heat Conduction Problem with Two Space Variables

I  V  Sergienko; O  N  Lytvyn; O  O  Lytvyn; V  I  Mezhuyev; L  S  Lobanova  and G  V  Zalyzhna

doi:10.17485/ijst/2015/v8i30/84753

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The Numerical Implementation of the Linear IntegroDifferential Equations Method for the Solution of Non-Stationary Heat Conduction Problem with Two Space Variables

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i30/84753

Year: 2015, Volume: 8, Issue: 30, Pages: 1-7

Original Article

The Numerical Implementation of the Linear IntegroDifferential Equations Method for the Solution of Non-Stationary Heat Conduction Problem with Two Space Variables

I. V. Sergienko¹, O. N. Lytvyn², O. O. Lytvyn², V. I. Mezhuyev^3*, L. S. Lobanova² and G. V. Zalyzhna²

¹ Institute of Cybernetics of the National Academy of Science, Kyiv, Ukraine
² Ukrainian Engineering and Pedagogical Academy, Kharkiv, Ukraine
³ University Malaysia Pahang, Gambang, Malaysia [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The paper proposes a general method for solution of non-stationary heat conduction problem with two space variables. It is based on Finite Element Method, which uses the operator of the interlination on a given system of lines. The region of consideration divided on rectangular or triangular elements with curvilinear sides belonging to the boundary of the domain. Interlineation of functions is a restoration of the function with the help of its traces on the system of lines. Operators of interlineations allow to restore functions of two or more variables between the lines using their traces and traces of their partial derivatives up to a given order on the indicated lines. Application of the method on examples of solutions of the nonstationary heat conduction equation for regions of complex shape is illustrated.
Keywords: Interlination of Functions, Initial-Boundary Value Problem, Linear Integro-Differential Equations, I NonStationary Heat Conduction Equation