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International Journal of Mathematical Research

October 2012, Volume 1, 1, pp 5-20

Collocation Approximation Methods for the Numerical Solutions of General nth Order Nonlinear Integro-Differential Equations by Canonical Polynomial

Taiwo O. A

,

Raji M. T

Taiwo O. A 1
Raji M. T 2

  1. Department of Mathematics, University of Ilorin 1

  2. Department of Mathematics and Statistics,the Poly. Ibadan 2

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Abstract:

In this Paper, a method based on the Tau method by canonical polynomials as the basis function is developed to find the numerical solutions of general nth order nonlinear integro-differential equations. The differential parts appearing in the equation are used to construct the canonical polynomials and the nonlinear cases are linearized by the Newton’s linearization scheme of order n and hence resulted to the use of iteration. Numerical examples are given to illustrate the effectiveness, convergence and the computational cost of the methods.

Contribution/ Originality

Keywords:


Reference:

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  12. Shahmorad, S. Ivaz and B. S. K. Mostahkam, "Newton-tau numerical solution of one dimensional non-linear integro-differential equations," Southeast Asian Bull. Math, vol. 33, pp. 733-740, 2009.

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