IJPAM: Volume 85, No. 3 (2013)
TWO-POINT BOUNDARY VALUE PROBLEMS
USING BLOCK METHOD
1,2,3Institute for Mathematical Research
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA
Abstract. This paper presents a direct two-point block one-step method for
solving linear Dirichlet boundary value problems (BVPs) directly.
The block method is formulated using Lagrange interpolating
polynomial. Mathematical problems which involve higher order
ordinary differential equations (ODEs) were likely to be reduced
into the system of first order equations in order to solve it.
However, this method will solve the second order linear Dirichlet
BVPs directly without reducing it to the system of first order
equations. The direct solution of the linear Dirichlet BVPs will
be calculated at the two-points simultaneously using constant step
size. This method will be used together with the linear shooting
technique to construct the numerical solution. The implementation
is based on the predictor and corrector formulas in the PE(CE)r
mode. Numerical results are given to show the efficiency and
performance of this method compared to the existing methods.
Received: January 24, 2013
AMS Subject Classification: 65L06, 65L10
Key Words and Phrases: linear Dirichlet boundary value problems, block method, linear shooting method, constant step size
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DOI: 10.12732/ijpam.v85i3.6 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 3