Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind

2012 ◽  
Vol 7 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Xianjuan Li ◽  
Tao Tang
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Collocation Methods ◽  
Spectral Collocation ◽  
Spectral Collocation Methods

scholarly journals Analysis of Generalized Multistep Collocation Solutions for Oscillatory Volterra Integral Equations

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2004
Author(s):  
Hao Chen ◽  
Ling Liu ◽  
Junjie Ma
Keyword(s):  
Error Estimate ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Oscillatory Integrals ◽  
Collocation Methods ◽  
Schur Polynomials ◽  
Numerical Tests ◽  
Highly Oscillatory ◽  
Highly Oscillatory Integrals

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.

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