A Numerical Approach Based on Taylor Polynomials for Solving a Class of Nonlinear Differential Equations

Abstract

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.

Numerical solutions of a class of nonlinear ordinary differential equations in Hermite series

“…In tab. 3, the exact solution of the problem and the the approximate solutions of the problem obtained with Taylor matrix method [19] and the proposed method on [0,1] x ∈ for 5 N = , are presented. Example 2.…”

“…In tab. 5, for N = 5, the solutions, exact and obtained with Taylor matrix method and suggested method, are compared [19]. as in the method given and n R of Example 2 is illustrated in fig.…”