4-stage, 3rd order SSP Runge-Kutta method.
@note Note On the current performance tests, this method shows 3rd order convergence, but its relative error is one order of magnitude higher than that obtained with other 3rd order methods. An implementation error cannot be excluded.
Main method: Kraaijevanger, Johannes Franciscus Bernardus Maria. "Contractivity of runge-kutta methods." BIT Numerical Mathematics 31.3 (1991): 482-528. DOI: 10.1007/BF01933264.
Embedded method: Conde, Sidafa, Imre Fekete, and John N. Shadid. "Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge--Kutta methods." arXiv preprint arXiv:1806.08693 (2018). arXiv: 1806.08693
Implementation: Ranocha, Hendrik, et al. "Optimized Runge-Kutta methods with automatic step size control for compressible computational fluid dynamics." Communications on Applied Mathematics and Computation 4.4 (2022): 1191-1228. arXiv:2104.06836
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(rkssp43_class), | intent(inout) | :: | me | |||
| real(kind=wp), | intent(in) | :: | t |
initial time |
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| real(kind=wp), | intent(in), | dimension(me%n) | :: | x |
initial state |
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| real(kind=wp), | intent(in) | :: | h |
time step |
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| real(kind=wp), | intent(out), | dimension(me%n) | :: | xf |
state at time |
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| real(kind=wp), | intent(out), | dimension(me%n) | :: | xerr |
truncation error estimate for |