Analytical approximations of one-dimensional hyperbolic equation with non-local integral conditions by reduced differential transform method

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O.Box 1914, Rasht, Iran.

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

Abstract

In this work, an initial-boundary value problem with a non-classic condition for the one-dimensional wave equation is presented and the reduced differential transform method is applied to ascertain the solution of the problem. We will investigate a new kind of non-local boundary value problems in which are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The advantage of this method is its simplicity in using, it solves the problem directly and straightforward without using perturbation, linearization, Adomian’s polynomial or any other transformation and gives the solution in the form of convergent power series with simply determinable components. Also, the convergence of the method is proved and seven examples are tested to shows the competency of our study.

Keywords

Computational Methods for Differential Equations
Volume 8, Issue 3
August 2020
Pages 537-552

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History

  • Receive Date: 28 September 2018
  • Revise Date: 17 April 2019
  • Accept Date: 12 May 2019

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