EXACT SOLUTIONS OF BOUNDARY-VALUE PROBLEMS
Ivan Dimovski1, Margarita Spiridonova2
1,2Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
1113 Sofia, BULGARIA

Abstract

A survey of an approach for obtaining explicit formulae for solving local and nonlocal boundary value problems (BVPs) for some linear partial differential equations is presented. To this end an extension of the Heaviside-Mikusiński operational calculus is used. A multi-dimensional operational calculus is constructed for each of the considered problems. The main steps of construction of exact (closed) solutions using such operational calculi are outlined. It is based on a combination of the Fourier method and an extension of the Duhamel principle to the space variables. Program tools for numerical computation and visualization of the solutions using the computer algebra system Mathematica (http://www.wolfram.com/ mathematica) are developed.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 3
Year: 2018

DOI: 10.12732/ijam.v31i3.1

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