NUMERICAL METHOD FOR THE SOLUTION OF NONLINEAR BOUNDARY VALUE PROBLEMS (ODE)

The solution of a nonlinear boundary value problem in ordinary differential equations of the form L(x(t)) + f(x(t)) = 0 can be obtained by solving the associated system of nonlinear equations. In this paper, a three -step iterative method with ninth order convergence is proposed to solve the system of nonlinear equations. The scheme is kept free from second and higher order Frechet derivatives to make it computationally efficient . The nonlinear boundary value problem is discretized to produce a system of nonlinear equa-tions which is then solved using the proposed method. Later, the ninth order method is generalized to obtain a m-step scheme with 3m order of conver-gence. Standard problems like Bratu [3] one-dimensional problem and Frank-Kamenetzki [8] problem are solved using the new method. The performance of the new method is compared with an existing method [18] to establish its computational superiority.