Linear Barycentric Rational Collocation Method for Solving Non-Linear Partial Differential Equations

Jin, Li

doi:10.1007/s40819-022-01453-8

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…The barycentric Lagrange interpolation method and Crank-Nicolson scheme are combined to solve the two-dimensional Allen-Cahn equation [26]. In addition, the barycentric Lagrange interpolation method was used to solve telegraph equation [27], heat conduction equation [28], beam vibration equation [29], and so on.…”

Section: Introductionmentioning

confidence: 99%

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

Yuan,

Wang,

2024

J Nonlinear Math Phys

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In this paper, we deeply study the high-precision barycentric Lagrange interpolation collocation method to solve nonlinear wave equations. Firstly, we introduce the barycentric Lagrange interpolation and provide the differential matrix. Secondly, we construct a direct linearization iteration scheme to solve nonlinear wave equations. Once again, we use the barycentric Lagrange interpolation to approximate the (2+1) dimensional nonlinear wave equations and (3+1) dimensional nonlinear wave equations, and describe the matrix format for direct linearization iteration of the nonlinear wave equations. Finally, the comparative experiments show that the barycentric Lagrange interpolation collocation method for solving nonlinear wave equations have higher calculation accuracy and convergence rate.

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Section: Introductionmentioning

confidence: 99%

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

Yuan,

Wang,

2024

J Nonlinear Math Phys

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“…The primary advantage of the collocation approach is its versatility, making it applicable to a wide array of differential equation types. Notable instances of its application include ordinary DEs, as demonstrated in contributions such as [24], partial DEs showcased in [25,26], and FDEs illustrated through references such as [27,28].…”

Section: Introductionmentioning

confidence: 99%

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

Abd-Elhameed,

Youssri,

Amin

et al. 2023

Fractal Fract

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In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE). We introduce a new set of orthogonal polynomials (OPs) referred to as “Eighth-kind Chebyshev polynomials (CPs)”. These polynomials are special kinds of generalized Gegenbauer polynomials. To achieve the proposed numerical approximations, we first derive some new theoretical results for eighth-kind CPs, and after that, we employ the spectral collocation technique and incorporate the shifted eighth-kind CPs as fundamental functions. This method facilitates the transformation of the equation and its inherent conditions into a set of nonlinear algebraic equations. By harnessing Newton’s method, we obtain the necessary semi-analytical solutions. Rigorous analysis is dedicated to evaluating convergence and errors. The effectiveness and reliability of our approach are validated through a series of numerical experiments accompanied by comparative assessments. By undertaking these steps, we seek to communicate our findings comprehensively while ensuring the method’s applicability and precision are demonstrated.

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An algorithm for the Burgers’ equation using barycentric collocation method with a high-order exponential Lie-group scheme

Seydaoğlu

2022

Math Sci

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Linear Barycentric Rational Collocation Method for Solving Non-Linear Partial Differential Equations

Cited by 4 publications

References 25 publications

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

An algorithm for the Burgers’ equation using barycentric collocation method with a high-order exponential Lie-group scheme

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