Barycentric rational interpolation method for solving KPP equation

Jin Li; Yongling Cheng; Jin Li; Yongling Cheng

doi:10.3934/era.2023152

Electronic Research Archive

2023, Volume 31, Issue 5: 3014-3029. doi: 10.3934/era.2023152

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Barycentric rational interpolation method for solving KPP equation

Jin Li ,
Yongling Cheng ^,

School of Science, Shandong Jianzhu University, Jinan 250101, China

Received: 16 February 2023 Revised: 11 March 2023 Accepted: 12 March 2023 Published: 20 March 2023

In this paper, we seek to solve the Kolmogorov-Petrovskii-Piskunov (KPP) equation by the linear barycentric rational interpolation method (LBRIM). As there are non-linear parts in the KPP equation, three kinds of linearization schemes, direct linearization, partial linearization, Newton linearization, are presented to change the KPP equation into linear equations. With the help of barycentric rational interpolation basis function, matrix equations of three kinds of linearization schemes are obtained from the discrete KPP equation. Convergence rate of LBRIM for solving the KPP equation is also proved. At last, two examples are given to prove the theoretical analysis.
- barycentric rational interpolation,
- collocation method,
- Kolmogorov-Petrovskii-Piskunov equation,
- non linear PDE
Citation: Jin Li, Yongling Cheng. Barycentric rational interpolation method for solving KPP equation[J]. Electronic Research Archive, 2023, 31(5): 3014-3029. doi: 10.3934/era.2023152

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Abstract

In this paper, we seek to solve the Kolmogorov-Petrovskii-Piskunov (KPP) equation by the linear barycentric rational interpolation method (LBRIM). As there are non-linear parts in the KPP equation, three kinds of linearization schemes, direct linearization, partial linearization, Newton linearization, are presented to change the KPP equation into linear equations. With the help of barycentric rational interpolation basis function, matrix equations of three kinds of linearization schemes are obtained from the discrete KPP equation. Convergence rate of LBRIM for solving the KPP equation is also proved. At last, two examples are given to prove the theoretical analysis.

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