The symmetric compact finite difference method for nonlinear two-order boundary value problems

In this paper a symmetric compact finite difference method is presented for solving nonlinear two order two point boundary scheme of the form y″ = f(t, y) with boundary conditions y(a) = A, y(b) = B. The corresponding finite difference scheme with tridiagonal matrix is given by replacing the exponent terms by Padé approximation. Meanwhile, the error estimates of the method are established. Compared with other traditional methods, the advantages of the method are compact and simple. Several numerical examples are also given to show the validity and applicability of the method.