A high order convergence collocation method based on the reproducing kernel for general interface problems

Sun, Liang; Jing, Ning; Hou, Jinjiao

doi:10.1016/j.aml.2020.106718

Cited by 6 publications

(1 citation statement)

References 13 publications

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“…Xu and Lin [38] applied the RKM for solving the delay fractional differential equations. The RKM proposed by Geng and Cui [11] can be used to solve presented the RKM to solve the nonlocal fractional boundary value problems, in addition to the partial integro-differential equation, multi-point boundary value problems and so on, see [8,10,13,16,21,23,24,25,28,31,33,34,35,36,37,39,41] for more details. The aim of this article is to seek the approximate solutions of Equation (1.1) by the RKM and collocation method.…”

Section: Introductionmentioning

confidence: 99%

A Reproducing Kernel Method for Solving Singularly Perturbed Delay Parabolic Partial Differential Equations

Xie,

Zhang,

Niu

et al. 2023

Mathematical Modelling and Analysis

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In this article, we put forward an efficient method on the foundation of a few reproducing kernel spaces(RK-spaces) and the collocation method to seek the solution of delay parabolic partial differential equations(PDEs) with singular perturbation. The approximated solution to the equations is formulated and proved the exact solution is uniformly convergent by the solution. Furthermore, the partial differentiation of the approximated solution is also proved the partial derivatives of the exact solution is uniformly convergent by the solution. Meanwhile, we show that the accuracy of our method is in the order of T/n where T is the final time and n is the number of spatial (and time) discretization in the domain of interests. Three numerical examples are put forward to demonstrate the effectiveness of our presented scheme.

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