Matrix Approach To The Direct Computation Method For The Solution of Fredholm Integro-Differential Equations of The Second Kind With Degenerate Kernels

Nathaniel Mahwash Kamoh, Geoffrey Kumlengand, Joshua Sunday

Abstract


In this paper, a matrix approach to the direct computation method for solving Fredholm integro-differential equations (FIDEs) of the second kind with degenerate kernels is presented. Our approach consists of reducing the problem to a set of linear algebraic equations by approximating the kernel with a finite sum of products and determining the unknown constants by the matrix approach. The proposed method is simple, efficient and accurate; it approximates the solutions exactly with the closed form solutions. Some problems are considered using maple programme to illustrate the simplicity, efficiency and accuracy of the proposed method.

Keywords


Fredholm, matrix, direct solution, integro-differential equation, integral

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References


Abdul-Majid Wazwaz (2011): Linear and Nonlinear Integral Equations Methods and Applications. Higher Education Press, Beijing.

Pandey, P. K. (2015): Numerical Solution of Linear Fredholm Integro-Differential Equations by Non-standard Finite Difference Method, Applications and Applied Mathematics, An International Journal (AAM): (10)2, pp.1019-1026

Kamoh, N. M. and Kumleng, G. M. (2018): Developing a Finite Difference Hybrid Method for Solving Second Order Initial-Value Problems for the Volterra Type Integro-Differential Equations. Songklanakarin Journal of Science and Technology SJST-2018-0171.R1

Kamoh, N. M., Aboiyar, T. and Kimbir, A. R. (2017) Continuous Multistep Methods for Volterra Integro-Differential Equations of the Second Order, Science World Journal 12(3): pp.11-14

Kamoh, N. M. and Aboiyar, T. (2018) "Continuous linear multistep method for the general solution of first order initial value problems for Volterra integro-differential equations", Multidiscipline Modeling in Materials and Structures, Vol. 14 Issue: 5, pp.960-969, https://doi.org/10.1108/MMMS-12-2017-0149

D. C. Sharma and M. C. Goyal (2017): Integral Equations, PHI Private Learning Material Ltd, Delhi 110092.

Behrouz Raftari (2010): Numerical Solutions of the Linear Volterra Integro-differential Equations: Homotopy Perturbation Method and Finite Difference Method, World Applied Sciences Journal (9): pp. 7-12

Matinfar, M. and Riahifar, A. (2015): Numerical solution of Fredholm integral-differential equations on unbounded domain, Journal of Linear and Topological Algebra, 04(01):pp. 43- 52

Vahidi, A. R., Babolian, E., Cordshooli, Gh. A. and Azimzadeh, Z. (2009): Numerical Solution of Fredholm Integro-Differential Equation by Adomian’s Decomposition Method. International Journal of Mathematics Analysis, 3(36): pp.1769 – 1773

Saadatmandia, A. and Dehghan, B, (): Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients. Computers and Mathematics with Applications (59): pp.2996-3004

Nas, S., Yalcinbas, S. and Sezer, M. (2000): A Taylor polynomial approach for solving high order linear Fredholm integro-differential equations, International Journal of Mathematics Education Science Technology 31 (2): pp.213-225.

Sezer, M. and Gulsu, M. (2007): Polynomial solution of the most general linear Fredholm-Volterra integro differential-difference equations by means of Taylor collocation method, Applied Mathematics and Computation, (185): pp. 646-657.

Sezer, M. and Gulsu, M. (2005): A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument, Applied Mathematics and Computation (171): pp.332-344.

Behiry, S. H. and Hashish, H. (2002): Wavelet methods for the numerical solution of Fredholm integro-differential equations, International Journal of Applied Mathematics 11 (1): pp. 27-35.

Wazwaz, A.M. (2001): A reliable algorithm for solving boundary value problems for higher-order integro-differential equations, Applied Mathematics and Computation (118): pp.327-342.

Hosseini, S.M. and Shahmorad, S. (2003): Numerical solution of a class of Integro-Differential equations by the Tau Method with error estimation. Applied Mathematics and Computation (136):pp. 559–570




DOI: https://doi.org/10.18860/ca.v6i3.8960

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Copyright (c) 2020 Nathaniel Mahwash Kamoh, Geoffrey Kumlengand, Joshua Sunday

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