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README.md

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@@ -76,10 +76,28 @@ FOODIE is aimed to be a KISS-pure-Fortran library for integrating Ordinary Diffe
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+ [x] unfiltered leapfrog, 2nd order accurate, mostly unstable, see [4];
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+ [x] Robert-Asselin filtered leapfrog, 1st order accurate, see [4, 5, 6];
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+ [x] Robert-Asselin-Williams filtered leapfrog, 3rd order accurate, see [5, 6];
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+ [x] [Linear Multistep Methods SSP](http://fortran-foss-programmers.github.io/FOODIE/module/foodie_integrator_lmm_ssp.html) schemes see [16]:
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+ [x] [Linear Multistep Methods, SSP](http://fortran-foss-programmers.github.io/FOODIE/module/foodie_integrator_lmm_ssp.html) schemes see [16]:
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+ [x] 3 steps, 2nd order accurate;
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+ [x] 4 steps, 3rd order accurate;
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+ [x] 5 steps, 3rd order accurate;
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+ [x] [Linear Multistep Methods, SSP with Variable Step Size (VSS)](http://fortran-foss-programmers.github.io/FOODIE/module/foodie_integrator_lmm_ssp_vss.html) schemes see [17]:
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+ [x] 2 steps, 2nd order accurate;
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+ [x] 3 steps, 2nd order accurate;
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+ [x] 3 steps, 3rd order accurate;
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+ [x] 4 steps, 3rd order accurate;
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+ [x] 5 steps, 3rd order accurate;
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+ [ ] [Linear Multistep Runge-Kutta Methods SSP](http://fortran-foss-programmers.github.io/FOODIE/module/foodie_integrator_ms_runge_kutta_ssp.html) schemes see [18]:
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+ [x] 2 steps, 2 stages, 3rd order accurate;
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+ [x] 3 steps, 2 stages, 3rd order accurate;
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+ [ ] 4 steps, 3 stages, 5th order accurate;
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+ [ ] 3 steps, 6 stages, 5th order accurate;
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+ [ ] 3 steps, 5 stages, 6th order accurate;
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+ [ ] 3 steps, 7 stages, 7th order accurate;
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+ [ ] 4 steps, 7 stages, 7th order accurate;
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+ [x] 4 steps, 5 stages, 8th order accurate;
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+ [ ] 5 steps, 9 stages, 8th order accurate;
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+ [ ] 4 steps, 9 stages, 9th order accurate;
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+ [ ] 3 steps, 20 stages, 10th order accurate;
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+ [ ] Runge-Kutta schemes:
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+ [ ] [low-storage](http://fortran-foss-programmers.github.io/FOODIE/module/foodie_integrator_runge_kutta_low_storage.html) schemes, see [1, 2, 3]:
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+ [x] 1 stage, namely the forward explicit Euler scheme, 1st order accurate;
@@ -171,6 +189,10 @@ Any feature request is welcome.
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[16] *Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations*, S. Gottlieb, D. Ketcheson, C.W. Shu, 2011, 978-981-4289-26-9, doi:10.1142/7498, World Scientific Publishing Co. Pte. Ltd.
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[17] *Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size*, Y. Hadjimichael, D. Ketcheson, L. Lóczi, A. Németh, 2016, SIAM J. Numer. Anal., 54(5), 2799–2832.DOI:10.1137/15M101717X.
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[18] *Explicit Strong Stability Preserving Multistep Runge-Kutta Methods*, C. Bresten, S. Gottlieb, Z. Grant, D. Higgs, D. Ketcheson, A. Nemeth, Mathematics of Computation, 2016, http://dx.doi.org/10.1090/mcom/3115.
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## Status [![Status](https://img.shields.io/badge/status-beta-orange.svg)]()

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