TY - JOUR
T1 - A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 424
EP - 446
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1125nm
UR - https://global-sci.org/intro/article_detail/nmtma/5912.html
KW - Neutral Volterra integro-differential equation, weakly singular kernel, Jacobi collocation discretization, convergence analysis.
AB - <p style="text-align: justify;">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.</p>