TY - JOUR
T1 - A Spectral Method for Pantograph-Type Delay Differential Equations and Its Convergence Analysis
AU - Ishtiaq Ali, Hermann Brunner & Tao Tang
JO - Journal of Computational Mathematics
VL - 2-3
SP - 254
EP - 265
PY - 2009
DA - 2009/04
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8571.html
KW - Spectral methods, Legendre quadrature formula, Pantograph-type delay differential equations, Error analysis, Exponential convergence.
AB - <p style="text-align: justify;">We propose a novel numerical approach for delay differential equations with vanishing
proportional delays based on spectral methods. A Legendre-collocation method is employed
to obtain highly accurate numerical approximations to the exact solution. It is
proved theoretically and demonstrated numerically that the proposed method converges
exponentially provided that the data in the given pantograph delay differential equation
are smooth.</p>