TY - JOUR
T1 - Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 419
EP - 438
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.m1028
UR - https://global-sci.org/intro/article_detail/nmtma/5976.html
KW - Second order Volterra integro-differential equations, Gauss quadrature formula, Legendre-collocation methods, convergence analysis.
AB - <p style="text-align: justify;">A class of numerical methods is developed for second order
Volterra integro-differential equations by using
a Legendre spectral approach. We provide a rigorous error analysis
for the proposed methods, which shows that the numerical errors
decay exponentially in the $L^\infty$-norm and $L^2$-norm.
Numerical examples illustrate the convergence and effectiveness of
the numerical methods.</p>