A numerical scheme for solutions of a class of nonlinear differential equations

In this paper, a collocation method based on Bessel functions of the first kind is presented to compute the approximate solutions of a class of high-order nonlinear differential equations under the initial and boundary conditions. First, the matrix forms of the Bessel functions of the first kind and their derivatives are constructed. Second, by using these matrix forms, collocation points and the matrix operations, a nonlinear differential equation problem is converted to a system of nonlinear algebraic equations. The solutions of this system give the coefficients of the assumed approximate solution. To demonstrate the validity and applicability of the technique, numerical examples are included and comparisons are made with existing results. The results show the efficiency and accuracy of the present work.