--- a/scripts/ode/ode23.m	Fri Nov 11 09:20:00 2022 +0100
+++ b/scripts/ode/ode23.m	Fri Nov 11 08:31:11 2022 -0500
@@ -154,10 +154,6 @@
            "ode23: FCN must be a valid function handle");
   endif
 
-  ## FIXME: Warn user if ! isempty (funarguments)
-  ## Not a documented behavior and may be deprecated
-
-
   ## Start preprocessing, have a look which options are set in odeopts,
   ## check if an invalid or unused option is set.
   [defaults, classes, attributes] = odedefaults (numel (init),
@@ -245,7 +241,9 @@
     feval (odeopts.OutputFcn, [], [], "done", odeopts.funarguments{:});
   endif
   if (! isempty (odeopts.Events))   # Cleanup event function handling
-    ode_event_handler ([], [], [], [], [], "done");
+    ode_event_handler (odeopts.Events, solution.ode_t(end), ...
+                       solution.ode_x(end,:).', "done", ...
+                       odeopts.funarguments{:});
   endif
 
   ## Print additional information if option Stats is set
@@ -462,11 +460,11 @@
 %! opt = odeset ("Events", @fevn, "NormControl", "on");
 %! sol = ode23 (@fpol, [0 10], [2 0], opt);
 %! assert ([sol.ie, sol.xe, sol.ye.'],
-%!         [2.0, 2.496110, -0.830550, -2.677589], 1e-3);
+%!         [2.0, 2.496110, -0.830550, -2.677589], .5e-1);
 %!test  # Events option, five output arguments
 %! opt = odeset ("Events", @fevn, "NormControl", "on");
 %! [t, y, vxe, ye, vie] = ode23 (@fpol, [0 10], [2 0], opt);
-%! assert ([vie, vxe, ye], [2.0, 2.496110, -0.830550, -2.677589], 1e-3);
+%! assert ([vie, vxe, ye], [2.0, 2.496110, -0.830550, -2.677589], 1e-1);
 %!test  # Mass option as function
 %! opt = odeset ("Mass", @fmas);
 %! sol = ode23 (@fpol, [0 2], [2 0], opt);

--- a/scripts/ode/ode23s.m	Fri Nov 11 09:20:00 2022 +0100
+++ b/scripts/ode/ode23s.m	Fri Nov 11 08:31:11 2022 -0500
@@ -155,10 +155,6 @@
            "ode23s: FCN must be a valid function handle");
   endif
 
-  ## FIXME: Warn user if ! isempty (funarguments)
-  ## Not a documented behavior and may be deprecated
-
-
   ## Start preprocessing, have a look which options are set in odeopts,
   ## check if an invalid or unused option is set.
   [defaults, classes, attributes] = odedefaults (numel (init),
@@ -221,7 +217,9 @@
     feval (odeopts.OutputFcn, [], [], "done", odeopts.funarguments{:});
   endif
   if (! isempty (odeopts.Events))   # Cleanup event function handling
-    ode_event_handler ([], [], [], [], [], "done");
+    ode_event_handler (odeopts.Events, solution.ode_t(end), ...
+                       solution.ode_x(end,:).', "done", ...
+                       odeopts.funarguments{:});
   endif
 
   ## Print additional information if option Stats is set
@@ -458,15 +456,6 @@
 %! assert (sol.ie(1), 2);
 %! assert (isfield (sol, "xe"));
 %! assert (isfield (sol, "ye"));
-%!test  # Events option, now stop integration
-%! opt = odeset ("Events", @fevn, "NormControl", "on");
-%! sol = ode23s (@fpol, [0 10], [2 0], opt);
-%! assert ([sol.ie, sol.xe, sol.ye.'],
-%!         [2.0, 9.094439, -0.996480, -14.180147], 2e-2);
-%!test  # Events option, five output arguments
-%! opt = odeset ("Events", @fevn, "NormControl", "on");
-%! [t, y, vxe, ye, vie] = ode23s (@fpol, [0 10], [2 0], opt);
-%! assert ([vie, vxe, ye], [2.0, 9.094439, -0.996480, -14.180147], 2e-2);
 %!test  # Mass option as function
 %! opt = odeset ("Mass", @fmas);
 %! sol = ode23s (@fpol, [0 2], [2 0], opt);

--- a/scripts/ode/ode45.m	Fri Nov 11 09:20:00 2022 +0100
+++ b/scripts/ode/ode45.m	Fri Nov 11 08:31:11 2022 -0500
@@ -151,10 +151,6 @@
            "ode45: FCN must be a valid function handle");
   endif
 
-  ## FIXME: Warn user if ! isempty (funarguments)
-  ## Not a documented behavior and may be deprecated
-
-
   ## Start preprocessing, have a look which options are set in odeopts,
   ## check if an invalid or unused option is set
   [defaults, classes, attributes] = odedefaults (numel (init),
@@ -244,7 +240,9 @@
     feval (odeopts.OutputFcn, [], [], "done", odeopts.funarguments{:});
   endif
   if (! isempty (odeopts.Events))   # Cleanup event function handling
-    ode_event_handler ([], [], [], [], [], "done");
+    ode_event_handler (odeopts.Events, solution.ode_t(end), ...
+                       solution.ode_x(end,:).', "done", ...
+                       odeopts.funarguments{:});
   endif
 
   ## Print additional information if option Stats is set
@@ -473,12 +471,12 @@
 %! opt = odeset ("Events", @fevn, "NormControl", "on");
 %! sol = ode45 (@fpol, [0 10], [2 0], opt);
 %! assert ([sol.ie, sol.xe, sol.ye.'],
-%!         [2.0, 2.496110, -0.830550, -2.677589], 2e-3);
+%!         [2.0, 2.496110, -0.830550, -2.677589], 6e-1);
 %!test  # Events option, five output arguments
 %! opt = odeset ("Events", @fevn, "NormControl", "on");
 %! [t, y, vxe, ye, vie] = ode45 (@fpol, [0 10], [2 0], opt);
 %! assert ([vie, vxe, ye],
-%!         [2.0, 2.496110, -0.830550, -2.677589], 2e-3);
+%!         [2.0, 2.496110, -0.830550, -2.677589], 6e-1);
 %!test  # Mass option as function
 %! opt = odeset ("Mass", @fmas);
 %! sol = ode45 (@fpol, [0 2], [2 0], opt);

--- a/scripts/ode/private/integrate_adaptive.m	Fri Nov 11 09:20:00 2022 +0100
+++ b/scripts/ode/private/integrate_adaptive.m	Fri Nov 11 08:31:11 2022 -0500
@@ -121,9 +121,8 @@
   have_EventFcn = false;
   if (! isempty (options.Events))
     have_EventFcn  = true;
-    options.Events = @(t,y) options.Events (t, y, options.funarguments{:});
-    ode_event_handler (options.Events, tspan(1), ode_x, ...
-                       [], order, "init");
+    ode_event_handler (options.Events, tspan(1), ode_x,
+                       "init", options.funarguments{:});
   endif
 
   if (options.havenonnegative)
@@ -172,8 +171,8 @@
 
       ## Check for Events
       if (have_EventFcn)
-        solution.event = ode_event_handler ([], t_new, x_new, ...
-                                            new_k_vals, [], []);
+        solution.event = ode_event_handler (options.Events, t_new, x_new, ...
+                                            [], options.funarguments{:});
         ## Check for terminal Event
         if (! isempty (solution.event{1}) && solution.event{1} == 1)
           ode_t(istep) = solution.event{3}(end);
@@ -194,7 +193,8 @@
           iout = max (t_caught);
           output_x(:, t_caught) = ...
             runge_kutta_interpolate (order, [t_old t_new], [x_old x_new], ...
-                                     output_t(t_caught), new_k_vals);
+                                     output_t(t_caught), new_k_vals, dt, ...
+                                     fcn, options.funarguments);
         endif
         ## Add a possible additional output value if we found a terminal Event
         if ((terminal_event == true) && ...
@@ -210,7 +210,8 @@
         tadd = tadd(2:end);
         output_x(:, iout + (1:iadd)) = ...
           runge_kutta_interpolate (order, [t_old t_new], [x_old x_new], ...
-                                   tadd, new_k_vals);
+                                   tadd, new_k_vals, dt, fcn, ...
+                                   options.funarguments);
         output_t(iout + (1:iadd)) = tadd;
         iout = length (output_t);
       else                         # refine = 1

--- a/scripts/ode/private/ode_event_handler.m	Fri Nov 11 09:20:00 2022 +0100
+++ b/scripts/ode/private/ode_event_handler.m	Fri Nov 11 08:31:11 2022 -0500
@@ -24,45 +24,43 @@
 ########################################################################
 
 ## -*- texinfo -*-
-## @deftypefn {} {@var{retval} =} ode_event_handler (@var{@@evt_fcn}, @var{t}, @var{y}, @var{k_vals}, @var{ord}, @var{flag})
+## @deftypefn {} {@var{retval} =} ode_event_handler (@var{@@evtfcn}, @var{t}, @var{y}, @var{flag}, @var{par1}, @var{par2}, @dots{})
 ##
-## Return the solution of the event function (@var{@@evt_fcn}) which is
+## Return the solution of the event function (@var{@@evtfcn}) which is
 ## specified in the form of a function handle.
 ##
 ## The second input argument @var{t} is a scalar double and specifies the time
 ## of the event evaluation.
 ##
-## The third input argument @var{y} is a scalar or a column vector of type
-## double which specifies the solution(s) at time @var{t}.
+## The third input argument @var{y} may be a column vector of type double
+## (for ODEs and DAEs) which specifies the solutions.  Alternatives, @var{y}
+## may be a cell array (for IDEs and DDEs) which specifies the solutions and
+## derivatives.
 ##
-## The fourth input argument @var{k_vals} is a vector or matrix with the
-## k values obtained from the most recent integration step.
-##
-## The fifth input argument @var{ord} is the order of the integration technique.
-##
-## The sixth input argument @var{flag} is of type string.  Valid values are:
+## The fourth input argument @var{flag} is of type string.  Valid values are:
 ##
 ## @table @option
 ## @item  @qcode{"init"}
 ## Initialize internal persistent variables of the function
 ## @code{ode_event_handler} and return an empty cell array of size 4.
 ##
-## @item  @qcode{""}
-## (default) Evaluate the event function and return the solution @var{retval}
-## as a cell array of size 4. Inputs @var{ord} and @var{@@evt_fcn} are ignored,
-## since they are set in the @qcode{"init"} step.
+## @item  @qcode{"calc"}
+## Evaluate the event function and return the solution @var{retval} as a cell
+## array of size 4.
 ##
 ## @item  @qcode{"done"}
 ## Clean up internal variables of the function @code{ode_event_handler} and
-## return an empty cell array of size 4. All other inputs are ignored with
-## this flag.
+## return an empty cell array of size 4.
 ## @end table
 ##
+## If additional input arguments @var{par1}, @var{par2}, @dots{} are given
+## these parameters are passed directly to the event function.
+##
 ## This function is an ODE internal helper function and it should never be
 ## necessary to call it directly.
 ## @end deftypefn
 
-function retval = ode_event_handler (evt_fcn, t, y, k_vals, ord, flag = "")
+function retval = ode_event_handler (evtfcn, t, y, flag = "", varargin)
 
   ## No error handling has been implemented in this function to achieve
   ## the highest performance possible.
@@ -79,14 +77,23 @@
   ## yold    the ODE result
   ## retcell the return values cell array
   ## evtcnt  the counter for how often this function has been called
-  persistent evtold told yold retcell order evtfcn;
+  persistent evtold told yold retcell;
   persistent evtcnt = 1;   # Don't remove.  Required for Octave parser.
   persistent firstrun = true;
 
   if (isempty (flag))
     ## Process the event, i.e.,
     ## find the zero crossings for either a rising or falling edge
-    [evt, term, dir] = evtfcn (t, y);
+    if (! iscell (y))
+      inpargs = {evtfcn, t, y};
+    else
+      inpargs = {evtfcn, t, y{1}, y{2}};
+      y = y{1};  # Delete cell element 2
+    endif
+    if (nargin > 4)
+      inpargs = {inpargs{:}, varargin{:}};
+    endif
+    [evt, term, dir] = feval (inpargs{:});
 
     ## We require that all return values be row vectors
     evt = evt(:).'; term = term(:).'; dir = dir(:).';
@@ -112,21 +119,10 @@
         ## Add all events this step to the output.
         for idx2 = idx                      # Loop through all values of idx
           ## Calculate the time stamp when the event function returned 0 and
-          ## calculate new values for the integration results. We do both by
-          ## root solving, calling the Event function with y values from
-          ## the RK interpolation polynomial. Set tolerance to zero (actually
-          ## uses machine tolerance based criterion in this case) since we
-          ## don't have a way for the user to specify an acceptable tolerance.
-          ## For simple Event functions, this means we're basically root
-          ## finding on a small interval for a polynomial, so we expect
-          ## pretty quick convergence.
-          tvals = [told t];
-          yvals = [yold y];
-          tnew = fzero (@(t2) evtfcn_val (evtfcn, t2, ...
-                       runge_kutta_interpolate (order, tvals, yvals, ...
-                       t2, k_vals), idx2), tvals, optimset ("TolX", 0));
-          ynew = runge_kutta_interpolate (order, tvals, yvals, tnew, k_vals);
-
+          ## calculate new values for the integration results, we do both by
+          ## a linear interpolation.
+          tnew = t - evt(idx2) * (t - told) / (evt(idx2) - evtold(idx2));
+          ynew = (y - (t - tnew) * (y - yold) / (t - told)).';
           tnews(evtcntnew, 1) = tnew;
           ynews(evtcntnew, :) = ynew;
           terms(evtcntnew, 1) = term(idx2);
@@ -174,10 +170,17 @@
     ## a value for evtold.
 
     firstrun = true;
-    order = ord;
-    evtfcn = evt_fcn;
 
-    [evtold, ~, ~] = evtfcn (t, y);
+    if (! iscell (y))
+      inpargs = {evtfcn, t, y};
+    else
+      inpargs = {evtfcn, t, y{1}, y{2}};
+      y = y{1};  # Delete cell element 2
+    endif
+    if (nargin > 4)
+      inpargs = {inpargs{:}, varargin{:}};
+    endif
+    [evtold, ~, ~] = feval (inpargs{:});
 
     ## We require that all return values be row vectors
     evtold = evtold(:).'; told = t; yold = y;
@@ -187,15 +190,9 @@
   elseif (strcmp (flag, "done"))
     ## Clear this event handling function
     firstrun = true;
-    evtold = told = yold = evtcnt = order = evtfcn = [];
+    evtold = told = yold = evtcnt = [];
     retval = retcell = cell (1,4);
 
   endif
 
 endfunction
-
-function val = evtfcn_val (evtfcn, t, y, ind)
-  [evt, ~, ~] = evtfcn (t, y);
-  val = evt(ind);
-endfunction
-

--- a/scripts/ode/private/runge_kutta_interpolate.m	Fri Nov 11 09:20:00 2022 +0100
+++ b/scripts/ode/private/runge_kutta_interpolate.m	Fri Nov 11 08:31:11 2022 -0500
@@ -23,21 +23,22 @@
 ##
 ########################################################################
 
-function u_interp = runge_kutta_interpolate (order, z, u, t, k_vals)
+function u_interp = runge_kutta_interpolate (order, z, u, t, k_vals, dt, fcn, args)
 
   switch (order)
 
     case 1
-      ## Unused
       u_interp = interp1 (z, u.', t, "linear");
 
     case 2
-      ## ode23s with Rosenbrock scheme:
-      der = k_vals(:,1);
+      if (! isempty (k_vals))
+        der = k_vals(:,1);
+      else
+        der = feval (fcn, z(1) , u(:,1), args);
+      endif
       u_interp = quadratic_interpolation (z, u, der, t);
 
     case 3
-      ## ode23 with Bogacki-Shampine scheme:
       u_interp = hermite_cubic_interpolation (z, u, k_vals, t);
 
     case 5
@@ -45,10 +46,11 @@
       u_interp = hermite_quartic_interpolation (z, u, k_vals, t);
 
     otherwise
-      ## This should never happen
-      warning (["runge_kutta_interpolate: Invalid/unimplemented ", ...
-                "interpolation order: using linear interpolation instead"]);
-      u_interp = interp1 (z, u.', t, "linear");
+      warning (["High order interpolation not yet implemented: ", ...
+                "using cubic interpolation instead"]);
+      der(:,1) = feval (fcn, z(1), u(:,1), args);
+      der(:,2) = feval (fcn, z(2), u(:,2), args);
+      u_interp = hermite_cubic_interpolation (z, u, der, t);
 
   endswitch