An offset vector iteration method for solving two-point boundary-value problems

Abstract

An offset vector iteration technique is proposed for solving two-point boundary-value problems. In this paper the properties of the method are explored. Application to parameter selection is first considered and convergence properties are described; comparison is made with other numerical methods. The two-point boundary-value problem is shown to be equivalent to the parameter selection problem. The method generally has a lower convergence rate than second order techniques; however, in many applications each iteration requires relatively few computational operations. Therefore it is competitive with higher order numerical procedures in applications that require few iterations to obtain an acceptably accurate solution. A modification to the offset vector method is suggested which takes advantage of the finite difference information generated at each iteration. © 1968 The British Computer Society.