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Full-Text Articles in Physical Sciences and Mathematics
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 …
Nonic B-Spline Algorithms For Numerical Solution Of The Kawahara Equation, Meli̇s Zorşahi̇n Görgülü
Nonic B-Spline Algorithms For Numerical Solution Of The Kawahara Equation, Meli̇s Zorşahi̇n Görgülü
Turkish Journal of Mathematics
In this paper, the nonic (9th order) B-spline functions which have not been used before for the numerical solutions of the partial differential equations by finite element methods are used to solve numerically the Kawahara equation. These approaches involve the collocation and Galerkin finite element methods based on the nonic B-spline functions in space discretization and second order scheme (Crank-Nicolson method) in time discretization. To see the accuracy of the proposed methods three test problems are demonstrated and the obtained numerical results for both of the methods are compared with the exact solution of the Kawahara equation.