HIGH-ORDER NUMERICAL-METHOD FOR 2-POINT BOUNDARY-VALUE-PROBLEMS

In this paper the two-point boundary value problem is transformed into general first-order ordinary differential equation system through introduction of conditions of an integral character to supplement the simultaneous set of first-order equations. A new discrete approximation of a high-order compact difference scheme is presented for the first-order system. It is a block-bidiagonal profile and removes the limits of other high-order discrete schemes at the interval ends. The numerical tests of a seventh-order compact difference scheme show that the proposed scheme is very convenient and efficient for linear and nonlinear two-point boundary value problems. (C) 1995 Academic Press, Inc.