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On The Application Of Euler's Method To Linear Integro Differential Equations And Comparison With Existing Methods, Deni̇z Elmaci, Nurcan Baykuş Savaşaneri̇l, Fadi̇me Dal, Mehmet Sezer
On The Application Of Euler's Method To Linear Integro Differential Equations And Comparison With Existing Methods, Deni̇z Elmaci, Nurcan Baykuş Savaşaneri̇l, Fadi̇me Dal, Mehmet Sezer
Turkish Journal of Mathematics
In this study, a collocation method using Euler method for solving systems of linear integro-differential equations is presented. Thesolution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exactsolutions and solutions obtained by other methods show that the proposed method is an effective and highly promising for linear integro-differential equation systems. All of numerical calculations have been made on a computer using a program written in Matlab.
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
Turkish Journal of Mathematics
In this paper, a matrix-collocation method which uses the Euler polynomials is introduced to find the approximate solutions of singularly perturbed two-point boundary-value problems (BVPs). A system of algebraic equations is obtained by converting the boundary value problem with the aid of the collocation points. After this algebraic system, the coefficients of the approximate solution are determined. This error analysis includes two theorems which consist of an upper bound of errors and an error estimation technique. The present method and error analysis are applied to three numerical examples of singularly perturbed two-point BVPs. Numerical examples and comparisons with other methods …