Piecewise Polynomial Collocation for Volterra-type Integral Equations of the Second Kind

Abstract

The exact solution of a given integral equation of the second kind of Volterra type(with regular or weakly singular kernel) is projected into the space of (continuous) piecewise polynomials of degree m ≧ 1 and with prescribed knots by using collocation techniques. It is shown that a number of discrete methods for the numerical solution of such equations based on product integration techniques or on finite-difference methods are particular discrete versions of collocation methods of the above type. The error behaviour of approximate solutions obtained by collocation (including their discretizations) is discussed.