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A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel
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This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation
with a weakly singular kernel. The solution of this equation, even for analytic data, is
not smooth on the entire interval of integration. The Jacobi collocation discretization
is proposed for the given equation. A rigorous analysis of error bound is also provided
which theoretically justifies that both the error of approximate solution and the error of
approximate derivative of the solution decay exponentially in $L^∞$ norm and weighted $L^2$ norm. Numerical results are presented to demonstrate the effectiveness of the spectral
method.
Global Science Press
Title: A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel
Description:
This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation
with a weakly singular kernel.
The solution of this equation, even for analytic data, is
not smooth on the entire interval of integration.
The Jacobi collocation discretization
is proposed for the given equation.
A rigorous analysis of error bound is also provided
which theoretically justifies that both the error of approximate solution and the error of
approximate derivative of the solution decay exponentially in $L^∞$ norm and weighted $L^2$ norm.
Numerical results are presented to demonstrate the effectiveness of the spectral
method.
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