--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+time/ExplicitRungeKuttaSecondOrderDiscreteData.m	Tue Oct 02 13:43:33 2018 -0700
@@ -0,0 +1,129 @@
+classdef ExplicitRungeKuttaSecondOrderDiscreteData < time.Timestepper
+    properties
+        k
+        t
+        w
+        m
+        D
+        E
+        M
+        C_cont % Continuous part (function handle) of forcing on first order form.
+        C_discr% Discrete part (matrix) of forcing on first order form.
+        n
+        order
+        tsImplementation % Time stepper object, RK first order form,
+                         % which this wraps around.
+    end
+
+
+    methods
+        % Solves u_tt = Du + Eu_t + S by
+        % Rewriting on first order form:
+        %   w_t = M*w + C(t)
+        % where
+        %   M = [
+        %      0, I;
+        %      D, E;
+        %   ]
+        % and
+        %   C(t) = [
+        %      0;
+        %      S(t)
+        %   ]
+        % D, E, should be matrices (or empty for zero)
+        % They can also be omitted by setting them equal to the empty matrix.
+        % S = S_cont + S_discr, where S_cont is a function handle
+        % S_discr a matrix of data vectors, one column per stage.
+        function obj = ExplicitRungeKuttaSecondOrderDiscreteData(D, E, S_cont, S_discr, k, t0, v0, v0t, order)
+            default_arg('order', 4);
+            default_arg('S_cont', []);
+            default_arg('S_discr', []);
+            obj.D = D;
+            obj.E = E;
+            obj.m = length(v0);
+            obj.n = 0;
+
+            default_arg('D', sparse(obj.m, obj.m) );
+            default_arg('E', sparse(obj.m, obj.m) );
+
+            obj.k = k;
+            obj.t = t0;
+            obj.w = [v0; v0t];
+
+            I = speye(obj.m);
+            O = sparse(obj.m,obj.m);
+
+            obj.M = [
+                O, I;
+                D, E;
+            ];
+
+            % Build C_cont
+            if ~isempty(S_cont)
+                obj.C_cont = @(t)[
+                    sparse(obj.m,1);
+                    S_cont(t)
+                            ];
+            else
+                obj.C_cont = [];
+            end
+
+            % Build C_discr
+            if ~isempty(S_discr)
+                [~, nt] = size(S_discr);
+                obj.C_discr = [sparse(obj.m, nt);
+                                S_discr
+                ];
+            else
+                obj.C_discr = [];
+            end
+            obj.tsImplementation = time.ExplicitRungeKuttaDiscreteData(obj.M, obj.C_cont, obj.C_discr,...
+                                                                        k, obj.t, obj.w, order);
+        end
+
+        function [v,t,U,T,K] = getV(obj)
+            [w,t,U,T,K] = obj.tsImplementation.getV();
+
+            v = w(1:end/2);
+            U = U(1:end/2, :); % Stage approximations in previous time step.
+            K = K(1:end/2, :); % Stage rates in previous time step.
+            % T: Stage times in previous time step.
+        end
+
+        function [vt,t,U,T,K] = getVt(obj)
+            [w,t,U,T,K] = obj.tsImplementation.getV();
+
+            vt = w(end/2+1:end);
+            U = U(end/2+1:end, :); % Stage approximations in previous time step.
+            K = K(end/2+1:end, :); % Stage rates in previous time step.
+            % T: Stage times in previous time step.
+        end
+
+        function [a,b,c,s] = getTableau(obj)
+            [a,b,c,s] = obj.tsImplementation.getTableau();
+        end
+
+        % Returns quadrature weights for stages in one time step
+        function quadWeights = getTimeStepQuadrature(obj)
+            [~, b] = obj.getTableau();
+            quadWeights = obj.k*b;
+        end
+
+        % Use RK for first order form to step
+        function obj = step(obj)
+            obj.tsImplementation.step();
+            [v, t] = obj.tsImplementation.getV();
+            obj.w = v;
+            obj.t = t;
+            obj.n = obj.n + 1;
+        end
+    end
+
+    methods (Static)
+        function k = getTimeStep(lambda, order)
+            default_arg('order', 4);
+            k = obj.tsImplementation.getTimeStep(lambda, order);
+        end
+    end
+
+end
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