explicit estimation being tested

ExplicitEstimation2.m

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+function varargout=ExplicitEstimation2(dt,dtRatio,Itime,extrapolation,varargin)
+
+% varargout=ExplicitEstimation(dt,dtRatio,Itime,varargin)
+% explicit estimate using second-order variable time step Adams-Bashforth
+% http://lucan.me.jhu.edu/wiki/index.php/Second-order_variable_time_step_Adams-Bashforth_method
+%
+
+
+if isempty(extrapolation)
+    extrapolation='auto';
+end
+
+
+if isequal(extrapolation,'auto')
+    if Itime==1
+        extrapolation='constant';
+    elseif Itime==2
+        extrapolation='linear';
+    elseif Itime >= 3  % second-order variable time step Adams-Bashforth
+        extrapolation='quadratic';
+    end
+else
+    if Itime==2 && isequal(extrapolation,'quadratic')
+        extrapolation='linear';
+    end
+end
+
+if Itime==1
+    extrapolation='constant';
+end
+
+nInputs=nargin-4;
+nOutputs = nargout;
+varargout = cell(1,nOutputs);
+
+if nInputs~=3*nOutputs
+    error(' wrong number of inputs ')
+end
+
+switch extrapolation
+
+    case 'constant'
+
+
+        for I=1:nOutputs
+            varargout{I}=varargin{1+3*(I-1)};
+        end
+
+    case 'linear'
+
+        for I=1:nOutputs
+            varargout{I}=varargin{1+3*(I-1)}+dt*varargin{2+3*(I-1)};
+        end
+
+    case 'quadratic'
+
+        for I=1:nOutputs
+            varargout{I}=varargin{1+3*(I-1)}+dt*((1+0.5*dtRatio)*varargin{2+3*(I-1)}-0.5*dtRatio*varargin{3+3*(I-1)});
+        end
+
+
+end
+
+end

TestExplicitEstimate.m

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+
+
+F=ExplicitEstimationForUaFields(CtrlVar,F,F0,Fm1);
+
+
+[F1.ub,F1.vb,F1.ud,F1.vd,F1.h]=...
+    ExplicitEstimation(CtrlVar.dt,CtrlVar.dtRatio,CtrlVar.CurrentRunStepNumber,...
+    F0.ub,F0.dubdt,Fm1.dubdt,...
+    F0.vb,F0.dvbdt,Fm1.dvbdt,...
+    F0.ud,F0.duddt,Fm1.duddt,...
+    F0.vd,F0.dvddt,Fm1.dvddt,...
+    F0.h,F0.dhdt,Fm1.dhdt);
+
+
+
+
+%%
+clear all
+fVector=[1  ;2  ;3   ;4  ;  5 ; 6 ] ;
+
+t=      [1  ; 1.2 ; 3 ; 5.09999 ;  5.1 ; 5.7  ; 7 ; 8.5 ; 9.3] ;
+t=      [1  ; 1.2 ; 3 ; 5.0 ;  5.1 ; 5.10000001  ; 5.1002 ; 8.5 ; 9.3] ;
+fVector=t.^2; dfdtExact=2*t;
+%fVector=sin(t*2*pi/10/2);
+
+%fVector=t;
+
+dfdtm1=[]; dfdt=[]; dtm1=[]; dtRatio=[];
+
+Itime=6;
+
+dt=t(Itime+1)-t(Itime);
+f0=fVector(Itime) ;
+if Itime>1
+    dfdt=(fVector(Itime)-fVector(Itime-1))./(t(Itime)-t(Itime-1));
+    dtm1=t(Itime)-t(Itime-1);
+    f1m=fVector(Itime-1);
+end
+
+if Itime>2
+    dfdtm1=(fVector(Itime-1)-fVector(Itime-2))./(t(Itime-1)-t(Itime-2));
+end
+
+if Itime>1
+    dtRatio=dt/dtm1;
+end
+
+dfdt=dfdtExact(Itime);  dfdtm1=dfdtExact(Itime-1); 
+
+
+extrapolation='constant';
+extrapolation='linear';
+extrapolation='quadratic';
+
+f1=ExplicitEstimation2(dt,dtRatio,Itime,extrapolation,f0,dfdt,dfdtm1);
+
+fprintf('\n\n f1=%g \t %g\n',f1,fVector(Itime+1))