Numerical method for the solution of nonlinear boundary value Problems (ODE)

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