Invariant imbedding and the continuation method: a comparison†

Abstract

Two-point boundary-value problems (TPBVP) are frequently encountered in almost every branch of engineering and physical sciences. The conventional numerical solution of TPBVP is based on a trial and error iterative procedure, in order that missing initial conditions be obtained. The starting or guessed missing initial conditions must be, however, close to the correct ones before the iterative procedure will converge. Imbedding techniques, such as invariant imbedding and the continuation method, have the major advantage of reducing TPBVP into initial-value problems. In this paper the two imbedding techniques are presented and discussed as to their absolute and relative merits and shortcomings.