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DSolve has reached the maximum number of calculations

James James
Posted 1 month ago

I reached the maximum number of calculations when using DSolve to calculate differential equations, which makes it impossible to fully solve. How can I expand the number of calculations of DSolve?

Here is my codeļ¼š

system = {vi q[t] == l iL'[t] + vC[t], 
   vC'[t] == iL[t]/c - vC[t]/(r c), vC[0] == 0, iL[0] == 0};
control = {q[0] == 1, 
   WhenEvent[Mod[t, \[Tau]] == (2/3) \[Tau], q[t] -> 0], 
   WhenEvent[Mod[t, \[Tau]] == 0, q[t] -> 1]};
pars = {vi -> 24, r -> 22, l -> 2 10^-2, 
   c -> 1 10^-4, \[Tau] -> 2.5 10^-5};
sol = DSolve[{system, control} /. pars, {vC, iL, q}, {t, 0, .2}, 
   DiscreteVariables -> q];
a = Evaluate[iL[t] /. sol];
b = Evaluate[vC[t] /. sol];
Plot[a, {t, 0, 0.2}, AxesLabel -> {"s", "il[t]/A"}, 
 PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Red}, 
 PlotRange -> All]
Plot[b, {t, 0, 0.2}, AxesLabel -> {"s", "vc[t]/V"}, 
 PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Blue}, 
 PlotRange -> All]
POSTED BY: James James
7 Replies
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In this case I would try Piecewise instead of WhenEvent:

\[Tau] = 1/9;
pwQ[t_] = PiecewiseExpand[Boole[0 <= Mod[t, \[Tau]] < (2/3)*\[Tau]],
   0 <= t <= 3 \[Tau]];
spSystem = {vi  pwQ[t] == l  iL'[t] + vC[t],
   vC'[t] == iL[t]/c - vC[t]/(r  c),
   vC[0] == 0, iL[0] == 0};
pwSol = DSolve[system2, {vC, iL},
    {t, 0, 2/10}] // Simplify;
Simplify[spSystem /. pwSol[[1]] /.
  {{t -> 1/100}, {t -> 1/9 - 1/27 + 1/30}, {t -> 1/9 + 1/27}}]
POSTED BY: Gianluca Gorni
James James
James James
Posted 1 month ago
POSTED BY: James James

I didn't know about $MaxPienewiseCases. You can try increasing it Do you know in advance how many intervals you need? For a full analytical solution I would use exact numbers:

\[Tau] = 25/10 10^-4;
POSTED BY: Gianluca Gorni
James James
James James
Posted 1 month ago

Yes, I found the help document for

$MaxPickewiseCases

and directly set $MaxPickewiseCases=(the range you want). The link to the help document isenter link description here

But my code doesn't produce any results...

\[Tau] = 25/10 10^-4;
pwQ[t_] = 
  PiecewiseExpand[Boole[0 <= Mod[t, \[Tau]] < (2/3)*\[Tau]], 
   0 <= t <= 3/100];
$MaxPiecewiseCases = 200;
pars = {vi -> 24, r -> 22, l -> 2 10^-2, c -> 1 10^-4};
spSystem = {vi pwQ[t] == l iL'[t] + vC[t], 
   vC'[t] == iL[t]/c - vC[t]/(r c), vC[0] == 0, iL[0] == 0};
pwSol = DSolve[spSystem /. pars, {vC, iL}, {t, 0, 2/100}] // 
   Simplify;
a = Evaluate[iL[t] /. pwSol];
b = Evaluate[vC[t] /. pwSol];
Plot[a, {t, 0, 0.02}, AxesLabel -> {"s", "il[t]/A"}, 
 PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Red}, 
 PlotRange -> All]
Plot[b, {t, 0, 0.02}, AxesLabel -> {"s", "vc[t]/V"}, 
 PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Blue}, 
 PlotRange -> All]
POSTED BY: James James

Have you tried NDSolve instead of Solve?
POSTED BY: Gianluca Gorni
James James
James James
Posted 1 month ago

Because I want to obtain an exact solution, I am using DSolve instead of NDSolve.
POSTED BY: James James

With this kind of thinking, we have many thousands of pages of analytical solutions. Do you really need an analytical solution?

After calculations by DSolve, conclusions can be drawn ,solution looks off than numeric one ,maybe a bug in DSolve.

Even for parameter:

\[Tau] -> 2.5 10^-5

DSolve probably give you not correct solution.See attached file.

Regards M.I

Attachments:
Diff equation.nb
POSTED BY: Mariusz Iwaniuk
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