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Sunday, Joshua
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Education Mathematics

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MATRIX APPROACH TO THE DIRECT COMPUTATION METHOD FOR THE SOLUTION OF FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS OF THE SECOND KIND WITH DEGENERATE KERNELS Kamoh, Nathaniel Mahwash; Kumleng, Geoffrey; Sunday, Joshua
Unnes Journal of Mathematics Vol 9 No 2 (2020)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v9i2.38614

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
On the Efficient Approach for the Solution of General Second Order Linear and Nonlinear Fredholm Integro-Differential Equations Kamoh, Nathaniel; Sunday, Joshua; Simooyol, Comfort
Unnes Journal of Mathematics Vol. 13 No. 1 (2024): Unnes Journal of Mathematics Volume 1, 2024
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v13i1.12851

Abstract

In this paper, Fredholm integro-differential equations are solved using the derivative of the Lucas polynomials in matrix form. The equation is first transformed into systems of nonlinear algebraic equations using the Lucas polynomials. The unknown parameters required for approximating the solution of Fredholm integro-differential equations are then determined using Gaussian elimination. The method has proven to be an active and dependable technique for solving many Fredholm integro-differential equations of different order. The novelty in this technique is that it is capable of solving Fredholm integro differential equation of any order by simply updating the matrix of derivative of the Lucas polynomials also surprisingly the technique was tried on mix Fredholm-Volterra integro differential equation and the result obtained was amazing. Some test problems contained in the literature were solved using the developed technique and the results confirmed the applicability and efficiency of the method. The accuracy of the method was observed to be better when compared with some existing methods. 
Co-Authors Kamoh, Nathaniel Kamoh, Nathaniel Mahwash Kumleng, Geoffrey Simooyol, Comfort