| Abstract: | In this paper, we present Newton-like methods (modified Newton method and modified secant method), which explore the special structure of the finitedifference approximation of fourth order to the nonlinear two-point boundary value problems At each iteration, modified secant method only calls and computes one function vector (i.e., no additional cast in function evaluations), and it has a R- convergence rate, and modified Newton method only calls two function vectors,and it has a Q-quadratic convergence rate. At last, our numerical results show the new methods are very effective. |
