Improved coefficients for SSP(5,4).

Author: ketch

nodepy/runge_kutta_method.py

@@ -3190,12 +3190,19 @@ def loadRKM(which='All'):
                                          description='From Ruuth-Spiteri paper',
                                          shortname='SSPRK95')
     #================================================
+    # The coefficients given here are not exactly those from the original paper.
+    # They have been improved to be accurate to 30 digits; the original method
+    # coefficients are accurate only to about 10 digits.
     A = np.array([[0,0,0,0,0],
-                  [0.39175222700392,0,0,0,0],
-                  [0.21766909633821, 0.36841059262959, 0,0,0],
-                  [0.08269208670950, 0.13995850206999, 0.25189177424738, 0,0],
-                  [0.06796628370320, 0.11503469844438, 0.20703489864929, 0.54497475021237, 0]])
-    b = np.array([0.14681187618661, 0.24848290924556, 0.10425883036650, 0.27443890091960, 0.22600748319395])
+                  [0.391752226869253785640632115627,0,0,0,0],
+                  [0.217669096357834985920253802915, 0.368410592709066783214662112772, 0,0,0],
+                  [0.0826920866830935842609242437786, 0.139958502107426395108400626025, \
+                    0.251891774371960822884363746140, 0,0],
+                  [0.0679662835740483884329695316049, 0.115034698453668419467815057942, \
+                    0.207034898772936576352392025561, 0.544974750295139481064416383368, 0]])
+    b = np.array([0.146811876157875933686947006683, 0.248482909391317264243714136087, \
+                    0.104258830279481225354037031167, 0.274438901048480694917546480567, \
+                    0.226007483122844881797755345495])
     RK['SSP54'] = ExplicitRungeKuttaMethod(A,b,name='SSP 54',
                                            description='From Ruuth-Spiteri paper',
                                            shortname='SSPRK54')