Analysis of Generalized Multistep Collocation Solutions for Oscillatory Volterra Integral Equations

Hao Chen, Ling Liu and Junjie Ma
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Hao Chen: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Ling Liu: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Junjie Ma: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China

Mathematics, 2020, vol. 8, issue 11, 1-16

Abstract: In this work, we introduce a class of generalized multistep collocation methods for solving oscillatory Volterra integral equations, and study two kinds of convergence analysis. The error estimate with respect to the stepsize is given based on the interpolation remainder, and the nonclassical convergence analysis with respect to oscillation is developed by investigating the asymptotic property of highly oscillatory integrals. Besides, the linear stability is analyzed with the help of generalized Schur polynomials. Several numerical tests are given to show that the numerical results coincide with our theoretical estimates.

Keywords: collocation; volterra integral equation; highly oscillatory; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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