A High-Order Approximate Solution for the Nonlinear 3D Volterra Integral Equations with Uniform Accuracy

Abstract

In this paper, we present a high-order approximate solution with uniform accuracy for nonlinear 3D Volterra integral equations. This numerical scheme is constructed based on the three-dimensional block cubic Lagrangian interpolation method. At the same time, we give the local truncation error analysis of the numerical scheme based on Taylor’s theorem. Through theoretical analysis, we reach the conclusion that the optimal convergence order of this high-order numerical scheme is 4. Finally, we verify the effectiveness and applicability of the method through four numerical examples.

Keywords

• nonlinear Volterra integral equations
• high-order scheme
• optimal convergence order
• convergence analysis