Efficient Collocation Algorithm for Solving Three-Dimensional Linear and Nonlinear Volterra Integral Equations

This paper proposes a new approach to solving three-dimensional linear and nonlinear Volterra integral equations (3D-VIEs) of the second kind using the Taylor collocation method (TCM). We develop an algorithm utilizing Taylor polynomials to approximate solutions of 3D-VIEs within a finite-dimensional space. Moreover, we perform convergence analysis to validate the efficacy of our method. Additionally, we show comparison examples to demonstrate the method’s effectiveness. The comparison highlights the efficiency and reliability of our approach.