A new B-spline collocation method for singular integro-differential equations of higher orders

Abstract

Two numerical schemes based on B-spline collocation method are presented for approximate solution of the systems of singular integro-differential equations of higher orders appearing in fracture problems with Steigmann–Ogden surface energy. It is shown that the resulting systems of linear equations are well-conditioned and the numerical examples are in good agreement with known solutions. Although this paper is concerned with the numerical solution to the specific equations, the proposed method can be easily generalized to a large class of singular integro-differential equations.