Optimal error estimate of accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels
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In this paper, we investigate and analyze numerical solutions for the Volterra integrodifferential equations with tempered multi-term kernels. Firstly we derive some regularity estimates of the exact solution. Then a temporal-discrete scheme is established 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 singular behavior of the exact solution at t=0. Based on deduced regularity conditions, we prove that the proposed scheme is unconditionally stable and conservative, and possesses accurately temporal second-order convergence in L_2-norm. Numerical examples confirm the effectiveness of the proposed method.
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