Linear barycentric rational collocation method for solving generalized Poisson equations

Jin Li; Yongling Cheng; Zongcheng Li; Zhikang Tian; Jin Li; Yongling Cheng; Zongcheng Li; Zhikang Tian

doi:10.3934/mbe.2023221

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4782-4797. doi: 10.3934/mbe.2023221

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Linear barycentric rational collocation method for solving generalized Poisson equations

1.
School of Science, Shandong Jianzhu University, No. 1000 Fengming Road, Lingang Development Zone, Jinan 250101, Shandong, China
2.
Lab Master at School of Computer Science and Technology, Shandong Jianzhu University, No. 1000 Fengming Road, Lingang Development Zone, Jinan 250101, Shandong, China

Academic Editor: Feliz Minhós

Received: 29 November 2022 Revised: 19 December 2022 Accepted: 21 December 2022 Published: 03 January 2023

We consider the Poisson equation by collocation method with linear barycentric rational function. The discrete form of the Poisson equation was changed to matrix form. For the basis of barycentric rational function, we present the convergence rate of the linear barycentric rational collocation method for the Poisson equation. Domain decomposition method of the barycentric rational collocation method (BRCM) is also presented. Several numerical examples are provided to validate the algorithm.
- linear barycentric rational function,
- collocation method,
- error functional,
- poisson equation,
- barycentric rational function
Citation: Jin Li, Yongling Cheng, Zongcheng Li, Zhikang Tian. Linear barycentric rational collocation method for solving generalized Poisson equations[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4782-4797. doi: 10.3934/mbe.2023221

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Abstract

We consider the Poisson equation by collocation method with linear barycentric rational function. The discrete form of the Poisson equation was changed to matrix form. For the basis of barycentric rational function, we present the convergence rate of the linear barycentric rational collocation method for the Poisson equation. Domain decomposition method of the barycentric rational collocation method (BRCM) is also presented. Several numerical examples are provided to validate the algorithm.

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