Solving high-order nonlinear differential equations using operational matrix based on exponential collocation method

In this paper, the exponential approximation is applied to solve high-order nonlinear differential equations. The main idea of this method is based on the matrix representations of the exponential functions and their derivatives by using collocation points. To indicate the usefulness of this method we employ it for some well-known high-order nonlinear equations like Riccati, Lane-Emden and so on. The numerical approximate solutions are compared with available(existing) exact(analytical) solutions and the comparisons are made with other methods to show the accuracy of the proposed method. For convergence and error analysis of the method, criteria for a number of basis sentences presented. The method has been reviewed by several examples to show its validity and reliability. The reported examples illustrate that the method is appropriately efficient and accurate.