On solving linear Fredholm integro-differential equations via finite difference-Simpson’s approach

Bashir Danladi Garba; Sirajo Lawan Bichi

doi:10.26637/MJM0802/0024

Abstract

In this paper, a combination of Finite difference-Simpson’s approach were applied to solve Linear Fredholm integro-differential equations of second kind by discritising the unknown function, which leads in generating a system of linear algebraic equations. The numerical results obtained from the proposed method were compared with exact solutions of the tested problems which show that the method derived is effective and promising when compared with some existing method in the literature and error estimation of the scheme was derived.

Keywords:

Error estimation, Finite difference equations, Fredholm integro-differential equation, Simpson’s Method.

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Bashir Danladi Garba Department of Mathematics, Kano University of Science and technology Wudil, Nigeria. https://orcid.org/0000-0002-6266-2443
Sirajo Lawan Bichi Department of Mathematics, Bayero University Kano, Nigeria.

Pages: 469-472
Date Published: 01-04-2020
Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)

Aruchunan. E and Sulaiman, Numerical Solution of FirstOrder Linear Fredholm Integro-Differential Equations using Conjugate Gradient Method, Curtin Sarawak $1 s t$ Int. Symposium on Geology, (2009), 11-13.

Darania. P and Ali Ebadian, A method for the numerical solution of the integro-differential equations, Appl. Math. and Comp., 188(2007), 657-668.

Wazwaz. A, Linear and Nonlinear Integral Equations Methods and Applications, Springer Heidelberg Dordrecht London New York.

Danfu. H, Xufeng. S, Numerical solution of integro differential equations by using CAS wavelet operational matrix of integration, Appl. math. and Comp., 194(2007), $460-466$.

Kurt. N, Sezer. M, Polynomial Solution of high order linear Fredholm Integro differential equations with constant coeffients, J. of Franklin institute, 345(2008), 839-850.

Rahman. M, Integral Equations and their Applications, Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK.

Saadati. R, B. Raftari. B, Adibi. H, Vaezpour. S, Shakeri. S, A comparison between Variational iteration method and Trapezoidal rule for solving LIDEs, World Appl. Sci. J. 4(3)(2008), 321-325 .

Vahidi. A, Babolian. E, Cordshooli. Gh, and Azimzadeh. $mathrm{Z}$, Numerical solution of FIDEs by Adomiandecompostion method, Int. J. of Math. Analy., 3(36)(2009), 17691773.

Pandey. P.K, Numerical Solution of Linear Fredholm Integro-Differential equations by Non-standard Finite Difference Method, Appl. and Appl. Math. 10(2)(2015), 1019-1026.

Manafianheris. J, Solving Integro-differential Equations Using the Modified Laplace Adomian Decomposition Method, J. of Math. Ext., 6(1)(2012), 41-55.

Mohammad. S, Hosseini, Shahmorad. S, Numerical piecewise approximate solution of Fredholm integrodifferential equations by the Tau method, Appl. Math. Model., 29(2005), 12-20.

Raftari. B, Numerical Solutions of the Linear Volterra Integro-differential Equations: Homotopy Perturbation Method and Finite Difference Method, World Appl. Sci. J. 9 (Spec. Issue of Appl. Math (2010).

Tamamagar M, The Numerical Solution of linear Fredholm integro-differential equations via Parametric iteration method, Appl. and Comput. Math., 3(2014), 4-10.

Jerri A. J, Introduction to Integral Equations with Applications, John Wiley and Sons, New York, (1999).

Alwaneh A, Al-Khaled K, Al-Towaiq M, Reliable Algorithms for Solving Integro-Differential Equations with Applications, Int. J. of Comput. Math., 87(2010), 15381554.