A method for solving nonlinear differential equations

The purpose of this paper is to present a method for solving nonlinear differential equations with constant and/or variable coefficients and with initial and/or boundary conditions.

The method converts the nonlinear boundary value problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.

The proposed technique allows us to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations.

The present approach provides a reliable technique, which avoids the tedious work needed by classical techniques and existing numerical methods. The nonlinear problem is solved without linearizing or discretizing the nonlinear terms of the equation. The method does not require physically unrealistic assumptions, linearization, discretization, perturbation, or any transformation in order to find the solutions of the given problems.