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Numerical Methods for a Volterra Integral Equation with Non-smooth Solutions

Diogo, Teresa; Lima, Pedro M.; Ford, Neville J.; Valtchev, Svilen S.

Journal of Computational and Applied Mathematics, 189(1-2) (2006), 412–423

We consider the numerical treatment of a singular Volterra integral equation with an infinite set of solutions, one of which is smooth and all others have infinite gradient at the origin. This equation has been the subject of previous works, where we have dealt with the approximation of the smooth solution. Here we present numerical methods which enable us to obtain approximations to any of the infinite class of solutions. Some numerical examples are given which illustrate the performance of the methods employed.