A composite Runge--Kutta method for the spectral solution of semilinear PDEs

DOI10.1006/jcph.2002.7127zbMath1015.65050OpenAlexW2075041225MaRDI QIDQ1868564

Tobin A. Driscoll

Publication date: 28 April 2003

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.2002.7127

zbMATH Keywords

nonlinear wavesnumerical examplesnonlinear Schrödinger equationCahn-Hilliard equationKuramoto-Sivashinsky equationRunge-Kutta methodsKorteweg-de Vries equationKadomtsev-Petviashvili equationFourier collocation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (15)

On stability and convergence of semi-Lagrangian methods for the first-order time-dependent nonlinear partial differential equations in 1D ⋮ Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves ⋮ Exponential time-differencing with embedded Runge-Kutta adaptive step control ⋮ An additive semi-implicit Runge--Kutta family of schemes for nonstiff systems ⋮ Numerical study of Davey–Stewartson I systems ⋮ Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations ⋮ Fourth-Order Time-Stepping For Stiff PDEs On The Sphere ⋮ Renormalized Reduced Order Models with Memory for Long Time Prediction ⋮ Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation ⋮ High precision numerical approach for Davey–Stewartson II type equations for Schwartz class initial data ⋮ Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation ⋮ Improved error bounds of the Strang splitting method for the highly oscillatory fractional nonlinear Schrödinger equation ⋮ On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions ⋮ On critical behaviour in systems of Hamiltonian partial differential equations ⋮ A numerical approach to Blow-up issues for Davey-Stewartson II systems

Cites Work

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• A PseudoSpectral Procedure for the Solution of Nonlinear Wave Equations with Examples from Free-Surface Flows
• Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations

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