IJPAM: Volume 85, No. 3 (2013)

NUMERICAL SOLUTION OF LINEAR DIRICHLET
TWO-POINT BOUNDARY VALUE PROBLEMS
USING BLOCK METHOD

Mohd Mughti Hasni1, Zanariah Abdul Majid2, Norazak Senu3
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