Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels

In this paper, we investigate and analyze numerical solutions for the Volterra inte -grodifferential equations with tempered multi-term kernels. Firstly, we derive some regularity estimates of the exact solution. Then a temporal-discrete scheme is estab-lished by employing Crank-Nicolson technique and product integration (PI) rule for discretizations of the time derivative and tempered-type fractional integral terms, respectively, from which, nonuniform meshes are applied to overcome the singu-lar behavior of the exact solution at t = 0. Based on deduced regularity conditions, we prove that the proposed scheme is unconditionally stable and possesses accurately temporal second-order convergence in L-2-norm. Numerical examples confirm the effectiveness of the proposed method.