SOLVING INTEGRO-DIFFERENTIAL EQUATIONS USING EXPONENTIALLY FITTED COLLOCATION APPROXIMATE TECHNIQUE(EFCAT)

Year 2019, Volume: 5 Issue: 1, 73 - 85, 26.06.2019

Falade Iyanda

https://doi.org/10.23884/mejs.2019.5.1.08

Cited By: 1

Abstract

In this paper, both linear Volterra and Fredholm integro-differential equations are considered. We
propose  and  implement Exponentially  Fitted Collocation  Approximate Technique  (EFCAT) to  solve
these types of equations. The collocated perturbed Integro-differential equations were transformed in
to square matrix form which eventually solved using MAPLE 18 software. In order to investigate the
accuracy of the solution with a finite number of computation length (N=8 and N=10) four examples
were considered. To show the efficiency of the present method, numerical experiments are performed
on some applied problems which have been solved by some existing methods and the numerical solutions
are  compared with available results in the literature  and that of analytical solution. The numerical
results obtain show the simplicity and efficiency of the method.

Keywords

Volterra and Fredholm integro-differential equations, exponentially fitted collocation approximate technique, analytical solution

References

• [1] P. Linz, Analytic and Numerical Methods for Volterra Equations, SIAM, Philadelphia, Pa, USA, Pp 132-139 1985.
• [2] G. Adomian, “Solving Frontier problems of physics: The decomposition method”, Kluwer Pp 123-134 1994.
• [3] J.H. He, “Homotopy perturbation technique”, Comput. Meth. Appl. Mech. Eng., 178 pp. 257-2621999.
• [4] J.H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media”, Computer. Meth. Appl. Mech. Engn., 167 pp 57-68. 1998.
• [5] O.A. Taiwo, K.I. Falade and A. K. Bello “Application of Collocation Methods for the numerical solution of Integro – Differential Equations by Chebyshev Polynomials”, Intern. Journal of Biological and Physical Sciences vol.16, pp12 – 20 2011.
• [6] R. Kanwall, K. Liu. “A Taylor expansion approach for solving integral equations”. International Journal of Mathematical Education in Science and Technology, vol 20: pp 411–414. 1989.
• [7] S. Yuzbasi, N. Sahin, M. Sezer. “Bessel polynomial solutions of high-order linear Volterra integrodifferentia lequations”. Computers & Mathematics with Applications, 62: pp. 1940–1956. 2011.
• [8] Falade K.I, “Numerical Solution of Higher Order Singular Initial Value Problems (SIVP) by Exponentially Fitted Collocation Approximate” Method American International Journal of Research in Science, Technology, Engineering & Mathematics, 21(1), -February 2018, pp. 48-55 December 2017.
• [9] Olumuyiwa A. Agbolade and Timothy A. Anake “Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method” Hindawi Journal of Applied Mathematics, Article ID 1510267, page 3 2017.
• [10] S. Alao, F.S. Akinboro, F.O. Akinpelu, R.A. Oderinu Numerical “Solution of Integro-Differential Equation Using Adomian Decomposition and Variational Iteration Methods.” IOSR Journal of Mathematics (IOSR- Volume 10, Issue 4 Ver. II, Page 20. Jul-Aug. 2014.
• [11] Jalil Rashidinia and Ali Tahmasebi “Approximate solution of linear integro-differential equations by using modified Taylor expansion method” World Journal of Modelling and Simulation Vol. 9 No. 4, page 300 2013.