Solving two point boundary value problems for ordinary differential equations using exponential finite difference method
DOI :
https://doi.org/10.5269/bspm.v34i1.22424Mots-clés :
Two-point Boundary value problems, Exponential finite difference method, Fourth order finite difference methodRésumé
In this article, a new exponential finite difference scheme for the numerical solution of two point boundary value problems with Dirichlet's boundary conditions is proposed. The scheme is based on an exponential approximation of the Taylor expansion for the discretized derivative .The convergence of the scheme discussed under appropriate condition .The theoretical and numerical results show that this new scheme is efficient and at least fourth order accurate.
Références
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2. Stoer, J. and Bulirsch , R., Introduction to Numerical Analysis (2/e).Springer-Verlag, Berlin Heidelberg (1991).
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4. Van Niekerk, F.D., A nonlinear one step methods for initial value problems. Comp. Math. Appl. 13(1987), 367-371.
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10. Troesch, B.A., A simple approach to a sensitive two-point boundary value problem . J. Comput. Phys. 21 (1976), 279-290.
2. Stoer, J. and Bulirsch , R., Introduction to Numerical Analysis (2/e).Springer-Verlag, Berlin Heidelberg (1991).
3. Baxley, J. V., Nonlinear Two Point Boundary Value Problems in Ordinary and Partial Differential Equations (Everrit, W.N. and Sleeman, B.D. Eds.), Springer-Verlag, New York (1981), 46-54.
4. Van Niekerk, F.D., A nonlinear one step methods for initial value problems. Comp. Math. Appl. 13(1987), 367-371.
5. Pandey, P. K., Nonlinear Explicit Method for first Order Initial Value Problems. Acta Technica Jaurinensis, Vol. 6, No. 2 (2013), 118-125.
6. Collatz, L ., Numerical Treatment of Differential Equations (3/ed.). Springer Verlag, Berlin,(1966).
7. Jain, M. K., Iyenger, S. R. K. and Jain, R. K., Numerical Methods for Scientific and Engineering Computation (2/ed.). Wiley Eastern Ltd. New Delhi,(1987).
8. Varga , R. S., Matrix Iterative Analysis. Prentice Hall, Eaglewood Cliffs, N.J., USA (1962).
9. Golub, G. H. and Van Loan, C.F., Matrix Computations . John Hopkins University Press , Baltimore, USA (1989).
10. Troesch, B.A., A simple approach to a sensitive two-point boundary value problem . J. Comput. Phys. 21 (1976), 279-290.
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2014-10-01
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Research Articles
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