add Adams-Moulate ODE solver doc

Author: weberse2

src/functions-reference/higher-order_functions.Rmd

@@ -210,6 +210,21 @@ control parameters for the solver.
 Deprecated. Solves the ODE system for the times provided with a
 non-stiff solver. This calls the Runge Kutta Dopri algorithm.
 
+<!-- real[]; integrate_ode_adams; (function ode, real[] initial_state, real initial_time, real[] times, real[] theta, data real[] x_r, data int[] x_i); -->
+\index{{\tt \bfseries integrate\_ode\_adams }!{\tt (function ode, real[] initial\_state, real initial\_time, real[] times, real[] theta, data real[] x\_r, data int[] x\_i): real[]}|hyperpage}
+
+`real[]` **`integrate_ode_adams`**`(function ode, real[] initial_state, real initial_time, real[] times, real[] theta, data real[] x_r, data int[] x_i)`<br>\newline
+Solves the ODE system for the times provided using the Adams-Moulton
+method with the implementation from CVODES.
+
+<!-- real[]; integrate_ode_adams; (function ode, real[] initial_state, real initial_time, real[] times, real[] theta, data real[] x_r, data int[] x_i, data real rel_tol, data real abs_tol, dta int max_num_steps); -->
+\index{{\tt \bfseries integrate\_ode\_adams }!{\tt (function ode, real[] initial\_state, real initial\_time, real[] times, real[] theta, data real[] x\_r, data int[] x\_i, data real rel\_tol, data real abs\_tol, dta int max\_num\_steps): real[]}|hyperpage}
+
+`real[]` **`integrate_ode_adams`**`(function ode, real[] initial_state, real initial_time, real[] times, real[] theta, data real[] x_r, data int[] x_i, data real rel_tol, data real abs_tol, dta int max_num_steps)`<br>\newline
+Solves the ODE system for the times provided using the Adams-Moulton
+method with the implementation from CVODES with additional control
+parameters for the CVODES solver.
+
 ### Stiff Solver
 
 <!-- real[]; integrate_ode_bdf; (function ode, real[] initial_state, real initial_time, real[] times, real[] theta, data real[] x_r, data int[] x_i); -->

src/stan-users-guide/odes.Rmd

@@ -1,13 +1,17 @@
 # Ordinary Differential Equations  {#ode-solver.chapter}
 
 Stan provides a built-in mechanism for specifying and solving systems
-of ordinary differential equations (ODEs).  Stan provides two
-different integrators, one tuned for solving non-stiff systems and one
+of ordinary differential equations (ODEs).  Stan provides three
+different integrators, tuned for solving non-stiff systems and
 for stiff systems.
 
 * `rk45`: a fourth and fifth order Runge-Kutta method for
   non-stiff systems [@DormandPrince:1980; @AhnertMulansky:2011], and
 
+* `adams`: a variable-step, variable-order,
+  Adams-Moulton formula implementation for non-stiff systems
+  [@CohenHindmarsh:1996; @SerbanHindmarsh:2005]
+
 * `bdf`: a variable-step, variable-order,
   backward-differentiation formula implementation for stiff systems
   [@CohenHindmarsh:1996; @SerbanHindmarsh:2005]