Spectral collocation methods for nonlinear weakly singular Volterra integro-differential equations

2018 ◽  
Vol 35 (2) ◽  
pp. 576-596 ◽  
Author(s):  
Xiulian Shi ◽  
Yunxia Wei ◽  
Fenglin Huang
Keyword(s):  
Differential Equations ◽  
Collocation Methods ◽  
Spectral Collocation ◽  
Weakly Singular ◽  
Spectral Collocation Methods

scholarly journals Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel

1998 ◽  
Vol 39 (3) ◽  
pp. 408-430 ◽  
Author(s):  
Chang Ho Kim ◽  
U Jin Choi
Keyword(s):  
Collocation Methods ◽  
Singular Kernel ◽  
Time Step ◽  
Spectral Collocation ◽  
Weakly Singular Kernel ◽  
Weakly Singular ◽  
Space Discretization ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral ◽  
Spectral Collocation Methods

AbstractWe propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.

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