A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions

Abstract

In this paper, a novel second-order method based on a change of variable and the symmetrical and repeated quadrature formula is presented for numerical solving second kind Volterra integral equations with non-smooth solutions. Applying the discrete Grönwall inequality with weak singularity, the convergence order O(N−2) in L∞ norm is proved, where N refers to the number of time steps. Numerical results are conducted to verify the efficiency and accuracy of the method.

Keywords

• volterra equations
• weakly singular kernels
• a discrete Grönwall inequality
• change of variable
• error analysis