In this study, a matrix method based on Taylor polynomials and collocation points is presented for the approximate solution of a class of nonlinear differential equations, which have many applications in mathematics, physics and engineering. By means of matrix forms of the Taylor polynomials and their derivatives, the technique we have used reduces the solution of the nonlinear equation with mixed conditions to the solution of a matrix equation which corresponds to a system of nonlinear algebraic equations with the unknown Taylor coefficients. On the other hand, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing results in literature.
The purpose of this paper is to present a Hermite polynomial approach for solving a high-order ODE with non-linear terms under mixed conditions. The method we used is a matrix method based on collocation points together with truncated Hermite series and reduces the solution of equation to solution of a matrix equation which corresponds to a system of non-linear algebraic equations with unknown Hermite coefficients. In addition, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing result in literature.
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