Convergence analysis of the Jacobi-collocation method for nonlinear weakly singular Volterra integral equations

摘要

In this work, we present an efficient spectral-collocation method for numerical solution of a class of nonlinear weakly singular Volterra integral equations. This type of equations typically has a singular behavior at the left endpoint of the interval of integration. For overcoming this non-smooth behavior, we apply the Jacobi-collocation method. The convergence analysis of the proposed method is investigated in the L∞ and the weighted L2 norms and the results of several numerical experiments are presented which support the theoretical results. The computed results are compared wherever possible with those already available in the literature.