ode45/23/23s: Implement Events, OutputFcn, & Refine options (bug #49408 and #63063) * scripts/ode/ode23.m: Remove disabling of Refine option with struct output. Modify solution struct to output two sets of solution variables: output_t, output_x and ode_t and ode_x, and transpose struct output variables for improved Matlab compatibility. Update BISTs and perform minor code formatting. * scripts/ode/ode23s.m: Make same changes as ode23.m. * scripts/ode/ode45.m: Make same changes as ode23.m. Remove comment indicating that Refine is not implemented. * scripts/ode/private/integrate_adaptive.m: Update internal handling of variables t and x, separating them into ode_t & ode_x for internal integration and output_t & output_x for function output or calls to OutputFcn. Replace prior attempt at Refine option with new implementation. Specify time output or Refine != 0 are both interpolated from internal variables (ode_t, ode_x) for output of non-struct variables and/or for use with OutputFcn. Improve event handling when multiple Events (including at least one terminal Event) are detected in a single simulation step so that all Events up to and including the first terminal one are reported, and final data point is set to that of terminal Event. Send multiple data points in a single call to OutputFcn if they are all interpolated from a single integration step. Remove warning for termination when term signal is received from Events or OutputFcn. Return both internal variables (ode_t, ode_x) and interpolated variables (output_t, output_x) to allow calling function to correctly return either struct or separate variables. * scripts/ode/private/ode_event_handler.m: Sort multiple Events in ascending time order when they are encountered in one integration step. Remove any events after the time of a terminal Event. * scripts/ode/odeset.m: Update docstring to remove indication that Refine is not implemented * scripts/ode/odeplot.m: Update docstring to indicate that input t can be a scalar or vector. Add file test. * etc/NEWS.8.md: Add descriptions of changes under General improvements and Matlab compatibility.

--- a/etc/NEWS.8.md	Wed Oct 05 12:03:52 2022 -0700
+++ b/etc/NEWS.8.md	Wed Oct 05 16:53:01 2022 -0400
@@ -29,6 +29,9 @@
   outward normal vectors.  Input type checking has also been added for
   improved error handling.
 
+- `Refine` option is now implemented in functions `ode45`, `ode23`, 
+  and `ode23s`.
+
 ### Graphical User Interface
 
 
@@ -75,6 +78,10 @@
   Object      | Property         | Default State
   ------------|------------------|------------
   `figure`    | `"dockcontrols"` | `"on"`
+  
+- `ode45`, `ode23`, and `ode23s` have improved results for options `Events`,
+  `OutputFcn`, and `Refine`, along with corrected orientation of struct 
+  outputs.
 
 ### Alphabetical list of new functions added in Octave 8