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

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 domain into large number of subdomains and using biquadratic Lagrangian interpolation each subdomain. The convergence high-order is rigorously established. We prove that solution converges to exact optimal order O(hx4??+hy4??) 0<?,?<1. Finally, experiments four examples are shown, support theoretical findings illustrate efficiency our proposed method.