Linear barycentric rational collocation method for solving a class of generalized Boussinesq equations

Zongcheng Li; Jin Li; Zongcheng Li; Jin Li

doi:10.3934/math.2023921

AIMS Mathematics

2023, Volume 8, Issue 8: 18141-18162. doi: 10.3934/math.2023921

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Linear barycentric rational collocation method for solving a class of generalized Boussinesq equations

Zongcheng Li ,
Jin Li ^,

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

Received: 07 March 2023 Revised: 08 May 2023 Accepted: 15 May 2023 Published: 25 May 2023
MSC : 65D30, 65D32, 65R20

This paper is concerned with solving a class of generalized Boussinesq shallow-water wave (GBSWW) equations by the linear barycentric rational collocation method (LBRCM), which are nonlinear partial differential equations (PDEs). By using the method of direct linearization, those nonlinear PDEs are transformed into linear PDEs which can be easily solved, and the corresponding differentiation matrix equations of their discretization linear GBSWW equations are also given by a Kronecker product. Based on the error estimate of a barycentric interpolation, the rates of convergence for numerical solutions of GBSWW equations are obtained. Finally, three examples are presented to show theoretical results.
- collocation method,
- barycentric rational interpolation,
- Boussinesq equation,
- nonlinear PDE,
- direct linearization
Citation: Zongcheng Li, Jin Li. Linear barycentric rational collocation method for solving a class of generalized Boussinesq equations[J]. AIMS Mathematics, 2023, 8(8): 18141-18162. doi: 10.3934/math.2023921

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Abstract

This paper is concerned with solving a class of generalized Boussinesq shallow-water wave (GBSWW) equations by the linear barycentric rational collocation method (LBRCM), which are nonlinear partial differential equations (PDEs). By using the method of direct linearization, those nonlinear PDEs are transformed into linear PDEs which can be easily solved, and the corresponding differentiation matrix equations of their discretization linear GBSWW equations are also given by a Kronecker product. Based on the error estimate of a barycentric interpolation, the rates of convergence for numerical solutions of GBSWW equations are obtained. Finally, three examples are presented to show theoretical results.

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