Comparative Analysis of Finite Difference Methods for Solving Second Order Linear Partial Differential Equations

E. E. Ndiyo; U. A. Abasiekwere

doi:https://doi.org/10.14445/22315373/IJMTT-V57P538

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 4 | Year 2018 | Article Id. IJMTT-V57P538 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P538

Comparative Analysis of Finite Difference Methods for Solving Second Order Linear Partial Differential Equations

E. E. Ndiyo, U. A. Abasiekwere

Citation :

E. E. Ndiyo, U. A. Abasiekwere, "Comparative Analysis of Finite Difference Methods for Solving Second Order Linear Partial Differential Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 4, pp. 277-283, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P538

Abstract

The Liebmann’s and Gauss Seidel finite difference methods of solution are applied to a two dimensional second order linear elliptic partial differential equation with specified boundary conditions.The analytical (exact) solution obtained shows that the error of the numerical solutions increases with the number of iterations and consequentlyhas strong effects on the accuracy of the solution.

Keywords

Liebmann’s iteration, Gauss Seidel iteration

References

[1] George E. F. and Wolfgang R.W.,Finite Difference Methods for PartialDifferential Equations,Applied Mathematics Series,JohnWiley and Sons Inc.,New York,1960
[2] Gilgarg, D. and Trudinger, Elliptic Partial Differential Equations of Second Order,second ed., Springer-Verly., 1993
[3] Courant, R., Friedrichs, K. and Lewy,H. On the Partial Differential Equations of Mathematical Physics.IBM Journal of Research and Development, Volume: 11, Issue: 2, 1967.
[4] Everstine, G .C., Numerical solutions of Partial Differential Equations, Gaithersburg, 2010.
[5] Smith,G. D, Numerical Solution of Partial Differential Equations.Finite Difference Methods.Newyork: Oxford University Press, 1985.
[6] Yang, W. Y.,Chung, W. C. S. and Morris, J., Applied Numerical Methods Using MATLAB, John Wiley & Sons, Inc., 2005
[7] Bazuye, F.E., Numerical Methods for undergraduate students, Nigeria;Avant-Garde Computers, 2011.