An Accurate Numerical Approach for Solving Initial-lntegro Value Problems

摘要

In this paper, we derive a Gauss-Lobatto collocation method to solve numerically parabolic equations subject to initial-integro conditions. The spatial approximation is based on a Gauss-Lobatto collocation method. Here, we use the Legendre polynomials as the space basis functions. The Legendre Gauss-Lobatto quadrature rule is investigated for treating the integrals which are given in the two-point boundary conditions. Meanwhile the approximation for time variable, we applied the implicit Runge-Kutta method of fourth order. Finally, numerical results with comparisons are provided to demonstrate the effectiveness of the proposed spectral algorithms.