Numerical solution of second order boundary value problem using rational method
Numerical methods that are based on rational functions or better known as rational methods were discovered 60 years ago when they were initially used to deal with problem whose solution possess singularity.Ever since then, a number of studies have discovered various types of rational methods and use...
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| Format: | Conference or Workshop Item |
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2015
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| Online Access: | http://repo.uum.edu.my/18739/ http://doi.org/10.1063/1.4932422 |
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| Summary: | Numerical methods that are based on rational functions or better known as rational methods were discovered 60 years ago when they were initially used to deal with problem whose solution possess singularity.Ever since then, a number of studies have discovered various types of rational methods and used them to solve more general first order initial value problems such as stiff problem and problem with oscillatory property.Previous studies showed the reliability of rational methods in solving first order initial value problem through numerical experimentations. In this article, we have investigated the solvability of several existing fourth order rational methods to second order boundary value problem by replacing it with a coupled of first order initial value problems. Such replacement yielded the shooting method.As part of the investigation, these rational methods were compared among themselves and also compared with the 4-stage fourth order explicit Runge-Kutta method.Numerical experimentations seemed to indicate that rational methods were more accurate than the Runge-Kutta method for the case of nonlinear boundary value problem but vice versa for the case of linear boundary value problem. |
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