--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+rv/+time/RungekuttaRvInstage.m	Fri Jul 05 18:12:10 2019 +0200
@@ -0,0 +1,79 @@
+classdef RungekuttaRvInstage < time.Timestepper
+    properties
+        F       % RHS of the ODE
+        k       % Time step
+        t       % Time point
+        v       % Solution vector
+        n       % Time level
+        coeffs  % The coefficents used for the RK time integration
+        RV      % Residual Viscosity
+        DvDt    % Function for computing the time deriative used for the RV evaluation
+    end
+
+    methods
+        function obj = RungekuttaRvInstage(F, k, t0, v0, RV, DvDt, order)
+            obj.F = F;
+            obj.k = k;
+            obj.t = t0;
+            obj.v = v0;
+            obj.n = 0;
+            % Extract the coefficients for the specified order
+            % used for the RK updates from the Butcher tableua.
+            [s,a,b,c] = time.rk.butcherTableau(order);
+            obj.coeffs = struct('s',s,'a',a,'b',b,'c',c);
+            obj.RV = RV;
+            obj.DvDt = DvDt;
+        end
+
+        function [v, t] = getV(obj)
+            v = obj.v;
+            t = obj.t;
+        end
+
+        function state = getState(obj)
+            dvdt = obj.DvDt(obj.v);
+            [viscosity,  Df, firstOrderViscosity, residualViscosity] = obj.RV.evaluate(obj.v, dvdt);
+            state = struct('v', obj.v, 'dvdt', dvdt, 'Df', Df, 'viscosity', viscosity, 'residualViscosity', residualViscosity, 'firstOrderViscosity', firstOrderViscosity, 't', obj.t);
+        end
+
+        % Advances the solution vector one time step using the Runge-Kutta method given by
+        % obj.coeffs, updating the Residual Viscosity in each Runge-Kutta stage
+        function obj = step(obj)
+            obj.v = rv.time.rungekuttaRV(obj.v, obj.t, obj.k, obj.F, obj.RV, obj.DvDt, obj.coeffs);
+            obj.t = obj.t + obj.k;
+            obj.n = obj.n + 1;
+        end
+    end
+
+    % Takes one time step of size dt using the rungekutta method
+    % starting from v and where the function F(v,t,RV) gives the
+    % time derivatives. coeffs is a struct holding the RK coefficients
+    % for the specific method. RV is the residual viscosity which is updated
+    % in between the stages and after the updated solution is computed.
+    methods (Static)
+    function v = rungekuttaRV(v, t , dt, F, RV, DvDt, coeffs)
+        % Move one stage outside to avoid branching for updating the
+        % residual inside the loop.
+        k = zeros(length(v), coeffs.s);
+        k(:,1) = F(v,t,RV.evaluateViscosity(v,DvDt(v)));
+
+        % Compute the intermediate stages k
+        for i = 2:coeffs.s
+            u = v;
+            for j = 1:i-1
+                u = u + dt*coeffs.a(i,j)*k(:,j);
+            end
+            k(:,i) = F(u,t+coeffs.c(i)*dt, RV.evaluateViscosity(u,DvDt(u)));
+        end
+
+        % Compute the updated solution as a linear combination
+        % of the intermediate stages.
+        u = v;
+        for i = 1:coeffs.s
+            u = u + dt*coeffs.b(i)*k(:,i);
+        end
+        v = u;
+    end
+
+
+end
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