--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+rv/+time/RungekuttaExteriorRv.m	Thu Jan 17 10:44:12 2019 +0100
@@ -0,0 +1,65 @@
+classdef RungekuttaExteriorRv < 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
+        
+        % Properties related to the residual viscositys
+        RV              % Residual Viscosity operator
+        v_prev          % Solution vector at previous time levels, used for the RV evaluation
+        DvDt            % Function for computing the time deriative used for the RV evaluation
+        lowerBdfOrder   % Orders of the approximation of the time deriative, used for the RV evaluation.
+                        % dictates which accuracy the boot-strapping should start from.
+        upperBdfOrder   % Orders of the approximation of the time deriative, used for the RV evaluation.
+                        % Dictates the order of accuracy used once the boot-strapping is complete.
+        
+        % Convenience properties. Only for plotting
+        viscosity % Total viscosity
+        residualViscosity % Residual viscosity
+        firstOrderViscosity % first order viscosity
+        dvdt % Evaluated time derivative in residual
+        Df % Evaluated flux in residual
+    end
+    methods
+
+        function obj = RungekuttaExteriorRv(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;
+            obj.dvdt = obj.DvDt(obj.v);
+            [obj.viscosity,  obj.Df, obj.firstOrderViscosity, obj.residualViscosity] = RV.evaluate(obj.v,obj.dvdt);
+        end
+
+        function [v, t] = getV(obj)
+            v = obj.v;
+            t = obj.t;
+        end
+
+        function state = getState(obj)
+            state = struct('v', obj.v, 'dvdt', obj.dvdt, 'Df', obj.Df, 'viscosity', obj.viscosity, 'residualViscosity', obj.residualViscosity, 'firstOrderViscosity', obj.firstOrderViscosity, 't', obj.t);
+        end
+
+        function obj = step(obj)            
+            obj.dvdt = obj.DvDt(obj.v);
+            [obj.viscosity, obj.Df, obj.firstOrderViscosity, obj.residualViscosity] = obj.RV.evaluate(obj.v,obj.dvdt);
+
+            % Fix the viscosity of the RHS function F
+            F_visc = @(v,t) obj.F(v,t,obj.viscosity);
+            obj.v = time.rk.rungekutta(obj.v, obj.t, obj.k, F_visc, obj.coeffs);
+            obj.t = obj.t + obj.k;
+            obj.n = obj.n + 1;
+        end
+    end
+end
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