High accurate pseudo-spectral Galerkin scheme for pantograph type Volterra integro-differential equations with singular kernels
作者：
Highlights：
• Jacobi spectral Galerkin method (JSGM) and Jacobi pseudo-spectral Galerkin method.
• (JPSGM) are treated in details for solving first order weakly singular pantograph type delayed IDEs.
• Several useful lemmas that can help us to prove the main theorems are provided from literature.
• Main theorems associated to both of the JSGM and JPSGM are investigated deeply and rigorously.
• Two numerical examples are provided (with superior results) with respect to a recent Jacobi spectral collocation method (JSCM).
摘要
•Jacobi spectral Galerkin method (JSGM) and Jacobi pseudo-spectral Galerkin method.•(JPSGM) are treated in details for solving first order weakly singular pantograph type delayed IDEs.•Several useful lemmas that can help us to prove the main theorems are provided from literature.•Main theorems associated to both of the JSGM and JPSGM are investigated deeply and rigorously.•Two numerical examples are provided (with superior results) with respect to a recent Jacobi spectral collocation method (JSCM).
论文关键词：Weak singularity,Volterra delay integro-differential equations,Jacobi polynomials,spectral and pseudo-spectral Galerkin methods,analysis of convergence
论文评审过程：Received 20 August 2020, Revised 12 November 2020, Accepted 29 November 2020, Available online 29 December 2020, Version of Record 29 December 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125866
