The solver method applied in solve_ivp should be set in parameters.py…

…. Running marlpde as from the previous commit led to 'RuntimeError: Encountered Not-A-Number (NaN) in evolution' (this is with 'LSODA'). Stability was added by providing the equivalent of a Jacobian sparsity matrix for 'LSODA' which is done by setting 'lband' and 'uband'. This not only provided stability but also led to a substantial performance increase!

marlpde/Evolve_scenario.py

@@ -95,7 +95,8 @@ def integrate_equations(**kwargs):
 
     sol, info = eq.solve(state, t_range=End_time, dt=dt, \
                          solver=kwargs["solver"], scheme=kwargs["scheme"],\
-                         method="LSODA", tracker=["progress", \
+                         method=kwargs["method"], lband=kwargs["lband"], \
+                         uband=kwargs["uband"], tracker=["progress", \
                          storage.tracker(kwargs["progress_tracker_interval"]),\
                          live_plots, data_tracker], \
                          backend=kwargs["backend"], ret_info=kwargs["retinfo"],\

marlpde/parameters.py

@@ -158,6 +158,14 @@ class Solver:
     # chosen py-pde's native "explicit" solver above.
     scheme: str   = "euler"
     adaptive: bool = True
+    # solve_ivp from scipy offers six methods. They can be set here.
+    method: str = "LSODA"
+    # Setting lband and uband for method="LSODA" leads to tremendous performance
+    # increase. See Scipy's solve_ivp documentation for background. Consider it
+    # equivalent to providing a sparsity matrix for the "Radau" and "BDF"
+    # implicit methods.
+    lband: int = 1
+    uband: int = 1
     backend: str = "numba"
     retinfo: bool = True