Characteristic-based schemes for dispersive waves. I: The method of characteristics for smooth solutions. (English) Zbl 0787.65066
A model of relaxing heat flow is studied. A method of characteristics is developed containing three free parameters depending on the stiffness ratio. It is shown that such “decoupled” schemes do not take into account the interaction between the wave families, and that no method of characteristics solution can be better than second-order accurate.
Next, “coupled” schemes are developed which account for the interactions. Two additional free parameters are obtained. It is demonstrated that now the results are enhanced by this coupling. Finally, numerical results for “decoupled” and “coupled” schemes are presented showing that the dispersion relationships can be useful qualitative tool for analysis of numerical algorithms for dispersive waves.
Next, “coupled” schemes are developed which account for the interactions. Two additional free parameters are obtained. It is demonstrated that now the results are enhanced by this coupling. Finally, numerical results for “decoupled” and “coupled” schemes are presented showing that the dispersion relationships can be useful qualitative tool for analysis of numerical algorithms for dispersive waves.
Reviewer: P.Y.Yalamov (Russe)
MSC:
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
Keywords:
smooth solutions; heat flow; method of characteristics; numerical results; algorithms; dispersive wavesReferences:
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