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Akrivis, Georgios; Smyrlis, Yiorgos-Sokratis

Linearly implicit schemes for a class of dispersive-dissipative systems. (English) Zbl 1223.65050

Calcolo 48, No. 2, 145-172 (2011).
The authors discuss linearly implicit schemes for a class of dispersive-dissipative systems. They first consider an implicit-explicit Euler scheme, and then they discuss a second order implicit-explicit backward difference formulas scheme. Finally, they apply their abstract results to four examples, namely, a simple system of ordinary differential equations, the dispersively modified Kuramoto-Sivashinsky equation, the Topper-Kawahara equations in two space dimensions, and to systems of Kuramoto-Sivashinsky type equations.
Reviewer: Seenith Sivasundaram (Daytona Beach)

Cited in 6 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics

Keywords:

dispersive-dissipative systems; semilinear parabolic equations; Kuramoto-Sivashinsky equation; linearly implicit schemes; backward differentiation formulas methods; error estimates; Topper-Kawahara equations

Software:

RODAS
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Full Text: DOI

References:

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