RKNG #1923
RKNG #1923
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| // This class solves ordinary differential equations of the form | ||
| // q″ = f(q, q′, t) | ||
| // using an embedded generalized Runge-Kutta-Nyström (RKNG) method. We follow |
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¯\_(ツ)_/¯
Fine (1987) says “Runge-Kutta-Nyström Generalized (RKNG)”.
Sharp and Fine (1992) say “generalized Runge-Kutta-Nyström (RKNG)”.
Dormand (1996) says “The designation ‘RKNG’ is used because the shorter ‘RKN’ abbreviation is usually reserved for formulae applicable to the special equation (14.2)”, and does not expand the acronym.
Murua (1998) says “RKNG” without expanding the acronym.
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| // Alternative notations use a and b for the velocity Runge Kutta matrix and | ||
| // weights: Murua (1998), Runge-Kutta-Nyström methods for general second Order | ||
| // ODEs with application to multi-body Systems, uses (c, α, a, β̂, b̂, β, b), |
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There is a hat above a comma here.
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Your font is bad and you should feel bad.
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Or more likely, GitHub's font is bad and it should feel bad.
| template<typename Method, typename Position> | ||
| EmbeddedExplicitGeneralizedRungeKuttaNyströmIntegrator<Method, Position>:: | ||
| EmbeddedExplicitGeneralizedRungeKuttaNyströmIntegrator() { | ||
| // the first node is always 0 in an explicit method. |
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| // The first stage of the Runge-Kutta-Nyström iteration. In the FSAL case, | ||
| // |first_stage == 1| after the first step, since the first RHS evaluation has | ||
| // already occured in the previous step. In the non-FSAL case and in the |
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Done (also for the RKNs).
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| class EmbeddedExplicitGeneralizedRungeKuttaNyströmIntegratorTest | ||
| : public ::testing::Test {}; | ||
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| // b̂ for the position weights of the high-order method; | ||
| // b̂′ for the velocity weights of the high-order method; | ||
| // b for the position weights of the low-order method; | ||
| // b′ for the velocity weights of the low-order method. | ||
| // See Dormand, El-Mikkawy and Prince (1986), | ||
| // Families of Runge-Kutta-Nyström formulae, for an example. | ||
| // Note that other notations exist for the weights: | ||
| // المكاوى and رحمو (2003), A new optimized non-FSAL embedded |
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Don't we use the latinized form from the papers?
| @@ -16,9 +16,9 @@ constexpr int FloorOfPowerOf2(int const n) { | |||
| return n == 0 ? 0 : n == 1 ? 1 : FloorOfPowerOf2(n >> 1) << 1; | |||
| } | |||
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| // Ceiling log2 of n. 8 -> 3, 7 -> 2. | |||
| // Ceiling log2 of n, or 0 for n = 0. 8 -> 3, 7 -> 2. | |||
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So that Estrin evaluation compiles for degree 0.
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retest this please |
First cut, more tests to come (probably for the RKN too, the existing tests don't check the order).
Fix a bug in EstrinEvaluator (could not evaluate constants).
It may make sense to factor the implementations of the RKN and RKNG method with some template magic to ignore the a′ in the former.