1. A reproducing kernel method for solving singularly perturbed delay parabolic partial differential equations
- Author
-
Ruifeng Xie, Jian Zhang, Jing Niu, Wen Li, and Guangming Yao
- Subjects
delay parabolic equation ,reproducing kernel method ,collocation method ,numerical solution ,Mathematics ,QA1-939 - Abstract
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.
- Published
- 2023
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