Legendre-Petrov-Galerkin Chebyshev spectral collocation method for second-order nonlinear differential equations

DOI10.3934/dcdsb.2022166OpenAlexW4293462048MaRDI QIDQ2099218

Qiyi Gao, Hua Wu

Publication date: 23 November 2022

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2022166

zbMATH Keywords

Chebyshev spectral collocationsecond-order nonlinear ODELegendre-Petrov-Galerkinspace-time spectral

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Algorithms for approximation of functions (65D15) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (1)

A space-time spectral method for solving the nonlinear Klein-Gordon equation

Uses Software

• RODAS

Cites Work

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• A collocation method for generalized nonlinear Klein-Gordon equation
• Laguerre-Gauss collocation method for initial value problems of second order ODEs
• Fourierization of the Legendre-Galerkin method and a new space-time spectral method
• An \(h-p\) version of the continuous Petrov-Galerkin finite element method for nonlinear Volterra integro-differential equations
• Legendre-Gauss collocation methods for ordinary differential equations
• Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations
• Short proof of a discrete Gronwall inequality
• Single and multi-interval Legendre \(\tau\)-methods in time for parabolic equations
• Runge-Kutta methods adapted to the numerical integration of oscillatory problems
• Space-time spectral element method for solution of second-order hyperbolic equations
• Space-time spectral element method for one-dimensional nonlinear advection-diffusion problems
• Legendre-Gauss-Radau collocation method for solving initial value problems of first order ordinary differential equations
• Legendre-tau-Galerkin and spectral collocation method for nonlinear evolution equations
• An \(h\)-\(p\) version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations
• Legendre spectral collocation method for second-order nonlinear ordinary/partial differential equations
• Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
• Space-time spectral method for two-dimensional semilinear parabolic equations
• A Collocation Method for Initial Value Problems of Second-Order ODEs by Using Laguerre Functions
• Spectral Methods in Time for Parabolic Problems
• Spectral Methods and Their Applications
• The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points
• Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries
• Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws
• Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
• Optimal Error Estimates of the Chebyshev--Legendre Spectral Method for Solving the Generalized Burgers Equation
• Spectral Methods in Time for Hyperbolic Equations
• Space‐time spectral collocation method for the one‐dimensional sine‐<scp>G</scp>ordon equation
• An L^∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems
• Spectral Methods
• Single and multi‐interval Legendre spectral methods in time for parabolic equations
• Four-stage symplectic and P-stable SDIRKN methods with dispersion of high order

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