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September 2013 Vol. 2
Issue 2
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Fadugba SE
Adegboyegun BJ
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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
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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
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Abstract |
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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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