Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs - presented by Prof. Chi-Wang Shu

Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs

Prof. Chi-Wang Shu

Slide at 56:39

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STABILITY OF TIME DISCRETIZATIONS FOR SEMI-DISCRETE HIGH ORDER SCHEMES FOR TIME-DEPENDENT PDES
The classical fourth order method: The classical fourth order method with four stages, which is widely used in practice due to its stage and order optimality, is unfortunately not covered under the framework. In ( Sht 0 val Applicat ), we found a counter example to show that the method is not strongly stable, but successively applying the method for two steps yields a strongly stable method with eight stages.

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References

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Z. Sun and C. Shu (2017) Stability of the fourth order Runge–Kutta method for time-dependent partial differential equations. Annals of Mathematical Sciences and Applications

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