(A) hermite collocation method for the weaklysingular second kind volterra integral equation

Abstract

Collocation type methods are studied for the numerical solution of the weakly singular Volterra integral equation of the second kind which has nonsmooth solution near zero. The solution is approximated near zero by a linear combination of powers of $t^{\frac{1}{2}}$, and away from zero by a cubic spline in the continuity class $C^1$. The method shows that the order of convergence depends on the behavior of the solution near zero and presents the exact order of convergence. Some numerical examples are included.