scholarly journals Convergence analysis of the multistep Legendre pseudo-spectral method for Volterra integral equations with vanishing delays

2017 ◽  
Vol 321 ◽  
pp. 284-301 ◽  
Author(s):  
Xiao-yong Zhang
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Spectral Method ◽  
Volterra Integral Equations ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

A Multistep Legendre Pseudo-Spectral Method for Nonlinear Volterra Integral Equations

2020 ◽  
Vol 21 (1) ◽  
pp. 23-35
Author(s):  
Zhang Xiao-Yong ◽  
Li Jun-Lin
Keyword(s):  
Integral Equations ◽  
Spectral Method ◽  
Single Step ◽  
Volterra Integral Equations ◽  
High Order Accuracy ◽  
Step Size ◽  
Efficient Manner ◽  
Long Time ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

AbstractIn this paper, we extend the single-step pseudo-spectral method for nonlinear Volterra integral equations of the second kind to the multistep pseudo-spectral method. We also analyze the convergence of the hp-version of the multistep pseudo-spectral method under the L2-norm, and the result shows that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. In addition, it is very suitable for long time calculations and large step size situations. Numerical experiments confirm the theoretical expectations.

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