High accurate convergent spectral Galerkin methods for nonlinear weakly singular Volterra integro-differential equations

This paper contributes to investigate the Jacobi spectral and pseudo-spectral Galerkin techniques solve a general form of nonlinear weakly singular Volterra integro-differential equations first order. By applying some suitable change variables, we have made solution mentioned be smooth. Then, by schemes, accurate solutions are computed efficiently. Rigorous convergence analysis associated with both approaches discussed in detail. Some numerical test problems given depict accuracy presented schemes respect recent approximate methods literature.