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

Boya Zhou and Xiujun Cheng ()
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Boya Zhou: School of Mathematics and Big Data, Foshan University, Foshan 528225, China
Xiujun Cheng: College of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China

Mathematics, 2023, vol. 11, issue 12, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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