COLLOCATION METHODS FOR WEAKLY SINGULAR 2ND-KIND VOLTERRA INTEGRAL-EQUATIONS WITH NON-SMOOTH SOLUTION

Collocation type methods are studied for the numerical solution of the weakly singular Volterra integral equation of the second kind: /TO = 8(0 + K(s,As))(t-s)-lds, t£[O,T], (1) Jo where the solution f(t) is assumed to have the form f{t) = z(t)+'V(f). X 4 being sufficiently smooth. The solution is approximated near zero by a linear combination of powers off1, and away from zero by the usual polynomial representation. Convergence is proved and many numerical experiments are carried out with examples from the literature. A comparison is made with a method of Brunner & Nersett (1981), originally developed for (1) with a smooth solution. Special attention is paid to the numerical approximation of the so-called moment integrals which emerge in the collocation scheme. © 1982 Acidemic Pros Inc. (London) Limited.