A class of efficient linearly implicit methods based on TASE operators for Volterra integral equations

Abstract

Abstract This paper presents a family of numerical methods for the solution of Volterra integral equations of the second kind. The proposed approach combines a class of Runge–Kutta methods for ordinary differential equations with TASE operators, backward differentiation formulas, and Gregory quadrature rules. Numerical experiments confirm the theoretical results on convergence order and linear stability, demonstrating the efficiency of the proposed methods for the solution of stiff problems.