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