Add Cvode Documentation

  - Also fixed wrong order in tooltip

Author: AnHeuermann

OMCompiler/SimulationRuntime/c/util/simulation_options.c

@@ -706,7 +706,7 @@ const char *SOLVER_METHOD_DESC[S_MAX] = {
   /* S_IRKSCO */        "irksco - own developed Runge-Kutta solver - implicit, step size control, order 1-2",
   /* S_DASSL */         "dassl - default solver - BDF method - implicit, step size control, order 1-5",
   /* S_IDA */           "ida - SUNDIALS IDA solver - BDF method with sparse linear solver - implicit, step size control, order 1-5",
-  /* S_CVODE */         "cvode - experimental implementation of SUNDIALS CVODE solver - BDF or Adams-Moulton method - step size control, order 1-5",
+  /* S_CVODE */         "cvode - experimental implementation of SUNDIALS CVODE solver - BDF or Adams-Moulton method - step size control, order 1-12",
   /* S_ERKSSC */        "rungekuttaSsc - Runge-Kutta based on Novikov (2016) - explicit, step size control, order 4-5 [experimental]",
   /* S_SYM_SOLVER */     "symSolver - symbolic inline Solver [compiler flag +symSolver needed] - fixed step size, order 1",
   /* S_SYM_SOLVER_SSC */ "symSolverSsc - symbolic implicit Euler with step size control [compiler flag +symSolver needed] - step size control, order 1",

doc/UsersGuide/source/solving.rst

@@ -73,6 +73,35 @@ solver and furthermore it has the following IDA specific flags:
 :ref:`idaNonLinConvCoef <simflag-idaNonLinConvCoef>`,
 :ref:`idaMaxErrorTestFails <simflag-idaMaxErrorTestFails>`.
 
+
+.. _sundials_cvode :
+
+CVODE
+~~~~~
+
+The CVODE solver is part of sundials: SUite of Nonlinear and
+DIfferential/ALgebraic equation Solvers :cite:`Hindmarsh:2005`.
+CVODE solves initial value problems for ordinary differential equation (ODE)
+systems with variable-order, variable-step multistep methods.
+
+In OpenModelica, CVODE uses a combination of Backward Differentiation
+Formulas (varying order 1 to 5) as linear multi-step method and a modified
+Newton iteration with fixed Jacobian as non-linear solver per default.
+This setting is advised for stiff problems which are very common for Modelica
+models.
+For non-stiff problems an combination of an Adams-Moulton formula (varying
+order 1 to 12) as linear multi-step method together with a fixed-point
+iteration as non-linear solver method can be choosen.
+
+Both non-linear solver methods are internal functions of CVODE and use its
+internal direct dense linear solver CVDense.
+For the Jacobian of the ODE CVODE will use its internal dense difference
+quotient approximation.
+
+CVODE has the following solver specific flags:
+:ref:`cvodeNonlinearSolverIteration <simflag-cvodeNonlinearSolverIteration>`,
+:ref:`cvodeLinearMultistepMethod <simflag-cvodeLinearMultistepMethod>`.
+
 Basic Explicit Solvers
 ~~~~~~~~~~~~~~~~~~~~~~
 
@@ -106,6 +135,7 @@ Experimental Solvers
 The following solvers are marked as experimental, mostly because they
 are till now not tested very well.
 
+- cvode - experimental implementation of SUNDIALS CVODE solver - BDF or Adams-Moulton method - step size control, order 1-12
 - rungekuttaSsc - Runge-Kutta based on Novikov (2016) - explicit, step-size control, order 4-5
 - irksco - Own developed Runge-Kutta solver - implicit, step-size control, order 1-2
 - symSolver - Symbolic inline solver (requires :ref:`--symSolver <omcflag-symSolver>`) - fixed step-size, order 1