An eighth order tridiagonal finite difference method for nonlinear two-point boundary value problems

Abstract

We present an eighth order finite difference method for the second order nonlinear boundary value problemy″=f(x, y), y(a)=A, y(b)=B; the method iseconomical in the sense that each discretization of the differential equation at an interior grid point is based on seven evaluations off. For linear differential equations, the scheme leads to tridiagonal linear systems. We showO(h ⁸)-convergence of the method and demonstrate computationally its eighth order.