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Full-Text Articles in Physical Sciences and Mathematics
Solution Of Nonlinear Ordinary Differential Equations With Quadratic And Cubic Terms By Morgan-Voyce Matrix-Collocation Method, Mehmet Tarakçi, Mustafa Özel, Mehmet Sezer
Solution Of Nonlinear Ordinary Differential Equations With Quadratic And Cubic Terms By Morgan-Voyce Matrix-Collocation Method, Mehmet Tarakçi, Mustafa Özel, Mehmet Sezer
Turkish Journal of Mathematics
Nonlinear differential equations have many applications in different science and engineering disciplines. However, a nonlinear differential equation cannot be solved analytically and so must be solved numerically. Thus, we aim to develop a novel numerical algorithm based on Morgan-Voyce polynomials with collocation points and operational matrix method to solve nonlinear differential equations. In the our proposed method, the nonlinear differential equations including quadratic and cubic terms having the initial conditions are converted to a matrix equation. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB. The solution of this method for …
Lerch Matrix Collocation Method For 2d And 3d Volterra Type Integral And Second Order Partial Integro Differential Equations Together With An Alternative Error Analysis And Convergence Criterion Based On Residual Functions, Seda Çayan, Mehmet Sezer
Lerch Matrix Collocation Method For 2d And 3d Volterra Type Integral And Second Order Partial Integro Differential Equations Together With An Alternative Error Analysis And Convergence Criterion Based On Residual Functions, Seda Çayan, Mehmet Sezer
Turkish Journal of Mathematics
In this study, second order linear Volterra partial integro-differential equation with two- and three-dimensional are solved by collocation method based on Lerch polynomials. This method is composed of the operational matrix and collocation methods, which are based upon the matrix forms of the Lerch polynomials with the parameter $\lambda$ and Taylor polynomials, and their derivatives and integrals. The approximate solutions of the mentioned equations are investigated in terms of the Lerch polynomials the different values of $\lambda$. Also, to verify the accuracy and efficiency of the present method, an alternative convergence criterion along with error analysis depending on residual function …