Global Advanced Research Journal of Physical and Applied Sciences (GARJPAS)

September 2013 Vol. 2(2), pp. 017-023
Copyright © 2013 Global Advanced Research Journals

 

Review

On some finite difference methods for solving initial-boundary value problems in partial differential equations

Fadugba SE1* and Adegboyegun BJ2

1Department of Mathematical Sciences, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria

2School of Mathematics and Statistics, Faculty of Informatics, University of Wollongong, Australia

*Corresponding author E-mail: emmasfad2006@yahoo.com

Accepted 13 September, 2013

Abstract

This paper presents some finite difference methods for solving initial-boundary value problems in partial differential equations namely explicit method, implicit method and Crank Nicolson method. Finite difference methods are used to solve partial differential equations by approximating the differential equations over the area of integration by a system of algebraic equations. We discuss the convergence of these methods in the context of the exact solution. Moreover Crank Nicolson method is unconditionally stable, more accurate and converges faster than its two counterparts, the explicit and implicit methods.

Keywords: Accuracy, Convergence, Crank Nicolson Method, Finite Difference Method, Explicit Method, Implicit Method.

2010 Mathematics Subject Classification: 30E25, 35K20, 49K40, 58K25, 65L20, 65N06, 65N12

 

 

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