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I tried two ways of substituting which should have be equivalent. The fist way is that I collected varsol and dvarsol in a global variable solGolbal then do the substituting, and the second way is that I collected varsol and dvarsol in a local variable solModule and then do the substituting.

-------The above code is fine. The problem occured in following lines. ------

 The problem confusing me is :

Why dpdxGlobal[t] has one more term than dpdxModule[t] as shown in the red box in my second figure?

I tried two ways of substituting which should have be equivalent.

(1) The fist way is that I collected varsol and dvarsol in a global variable solGolbal then do the substituting;

(2)The second way is that I collected varsol and dvarsol in a local variable solModule and then do the substituting.

------- The above code is fine. The problem occured in following lines.   ------

The problem confusing me is :

Why did dpdxGlobal[t] have one more term than dpdxModule[t], as shown in the red box in my second figure?

The results of these two ways I think should be the same, however they showd apparent difference as shown in the figure below.

compute[_] := Module[{solModule}, solModule = {varsol, dvarsol} // Flatten; solGolbal = {varsol, dvarsol} // Flatten; dpdxModule[t_] = Evaluate[(-1000 D[U, t] + S)[[5]] /. solModule]; dpdxGlobal[t_] = Evaluate[(-1000 D[U, t] + S)[[5]] /. solGolbal]; Print[solModule - solGolbal]; {dpdxModule[t], dpdxGlobal[t]}]; F[t_] = compute[1]; F[t] ParametricPlot[{{vp[t], F[t][[1]]}, {vp[t], F[t][[2]]}}, {t, 5 T, 6 T}, AspectRatio -> 1/GoldenRatio, PlotLegends -> {"use module solution", "use global solution"}] 

The results of these two ways I think should be the same, however they showd apparent difference (i.e., the global way has one more term than the local way, as shown in the red box in the figure below).

compute[_] := Module[{solModule}, (*local way*) solModule = {varsol, dvarsol} // Flatten;  dpdxModule[t_] = Evaluate[(-1000 D[U, t] + S)[[5]] /. solModule];  (*global way*)   solGolbal = {varsol, dvarsol} // Flatten; dpdxGlobal[t_] = Evaluate[(-1000 D[U, t] + S)[[5]] /. solGolbal]; Print[solModule - solGolbal]; {dpdxModule[t], dpdxGlobal[t]}]; F[t_] = compute[1];   F[t](*global way has one more term than local way*) ParametricPlot[{{vp[t], F[t][[1]]}, {vp[t], F[t][[2]]}}, {t, 5 T, 6 T}, AspectRatio -> 1/GoldenRatio, PlotLegends -> {"use module solution", "use global solution"}] 

As you can see, the problem should in the last several lines of code. Where did difference between the two results come from? and Why? Is this a possible bug?

The problem confusing me is :

Why dpdxGlobal[t] has one more term than dpdxModule[t] as shown in the red box in my second figure?