A Higher-Order Numerical Scheme for Two-Dimensional Nonlinear Fractional Volterra Integral Equations with Uniform Accuracy

Abstract

In this paper, based on the modified block-by-block method, we propose a higher-order numerical scheme for two-dimensional nonlinear fractional Volterra integral equations with uniform accuracy. This approach involves discretizing the domain into a large number of subdomains and using biquadratic Lagrangian interpolation on each subdomain. The convergence of the high-order numerical scheme is rigorously established. We prove that the numerical solution converges to the exact solution with the optimal convergence order O(hx4−α+hy4−β) for 0<α,β<1. Finally, experiments with four numerical examples are shown, to support the theoretical findings and to illustrate the efficiency of our proposed method.