A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS

• 来源期刊: 计算数学（英文版）
• 关键词: Spectral methods Legendre quadrature formula Pantograph-type delay differential equations Error analysis Exponential convergence
• 年，卷（期）: 2009,（2）
• 页码范围: 254-265
• 页数: 12页
• 语种: 英文

摘要

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.