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How to rectify the error occurred in solving differential equation? Such as Indeterminate expression 0.` Complex Infinity encountered and also want to use rangakutta method to solve this issue?

g1 = 1;
g = 1;
K1 = .5;
\[Omega]1 = .5; \[Alpha] = \[Pi]/3; T = 1; x0 = 1;
sol1x1xx = 
 NDSolve[{x1'[t] == 
 g1*Sqrt[10 x1[t]] Sin[
    x2[t]] (-0.5*Abs[x4[t]]^2*Cos[\[Alpha]] + 
     0.5*Conjugate[x3[t]]*x4[t]*Sin[\[Alpha]] + 
     0.5*Abs[x3[t]]^2*Cos[\[Alpha]] + 
     0.5*Conjugate[x4[t]]*x3[t]*Sin[\[Alpha]]) - 
  K1 Sin[x2[t]]*
   Sum[Sin[(1000 + 0.5)*(t - n)]/((2 Pi) Sin[(t - n x0)/2]), {n, 
     1, 10}], 
x2'[t] == (-g1/Sqrt[0.4*x1[t]]) Cos[
    x2[t]] (-0.5*Abs[x4[t]]^2*Cos[\[Alpha]] + 
     0.5*Conjugate[x3[t]]*x4[t]*Sin[\[Alpha]] + 
     0.5*Abs[x3[t]]^2*Cos[\[Alpha]] + 
     0.5*Conjugate[x4[t]]*x3[t]*Sin[\[Alpha]]) + x1[t], 
x3'[t] == ((-I*(x3[
         t] (0.5 \[Omega]1 + 
          0.5 g Sqrt[10 x1[t]] Cos[x2[t]]*Cos[\[Alpha]]) + 
       0.5 x4[t] g Sqrt[10 x1[t]] Cos[x2[t]]*Sin[\[Alpha]]))/
   Sqrt[(Abs[x3[t]]^2 + Abs[x4[t]]^2)]), 
x4'[t] == ((-I*(x4[
         t] (-0.5 \[Omega]1 - 
          0.5 g Sqrt[10 x1[t]] Cos[x2[t]]*Cos[\[Alpha]]) + 
       0.5 x3[t] g Sqrt[10 x1[t]] Cos[x2[t]]*Sin[\[Alpha]]))/
   Sqrt[(Abs[x3[t]]^2 + Abs[x4[t]]^2)]), x1[0] == N[\[Pi]/20], 
x2[0] == 0, x3[0] == 0, x4[0] == 1}, {x1, x2, x3, x4}, {t, 0, 
2 Pi}, Method -> "ExplicitEuler", StartingStepSize -> 0.0002, 
MaxSteps -> 10^6];
Plot[Evaluate[Abs[{x1[t], x2[t], x3[t], x4[t]}] /. sol1x1xx[[1]]], {t,
0.1, 2 Pi}, PlotLegends -> {x1, x2, x3, x4}, PlotRange -> All, 
PlotLabel -> Row[{"K1 = ", K1, "g1 = ", g1}], AxesLabel -> Automatic,
PlotRange -> All]
Improve this question
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3
  • $\begingroup$ Your code runs without problems for me. I have MMA version 12.1. Did you try with a new kernel? $\endgroup$
    – Daniel Huber
    May 18, 2021 at 20:17
  • $\begingroup$ g=0 it is giving an error. $\endgroup$
    – user68207
    May 19, 2021 at 5:02
  • $\begingroup$ Even with g=0 it runs with MMA version 12.1 as you can see below $\endgroup$
    – Daniel Huber
    May 19, 2021 at 8:27

1 Answer 1

Reset to default
2
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Clear["Globals`*"]
g1 = 1;
g = 0;
K1 = .5;
\[Omega]1 = .5; \[Alpha] = \[Pi]/3; T = 1; x0 = 1;
sol1x1xx = 
  NDSolve[{x1'[t] == 
     g1*Sqrt[10 x1[t]] Sin[
        x2[t]] (-0.5*Abs[x4[t]]^2*Cos[\[Alpha]] + 
         0.5*Conjugate[x3[t]]*x4[t]*Sin[\[Alpha]] + 
         0.5*Abs[x3[t]]^2*Cos[\[Alpha]] + 
         0.5*Conjugate[x4[t]]*x3[t]*Sin[\[Alpha]]) - 
      K1 Sin[x2[t]]*
       Sum[Sin[(1000 + 0.5)*(t - n)]/((2 Pi) Sin[(t - n x0)/2]), {n, 
         1, 10}], 
    x2'[t] == (-g1/Sqrt[0.4*x1[t]]) Cos[
        x2[t]] (-0.5*Abs[x4[t]]^2*Cos[\[Alpha]] + 
         0.5*Conjugate[x3[t]]*x4[t]*Sin[\[Alpha]] + 
         0.5*Abs[x3[t]]^2*Cos[\[Alpha]] + 
         0.5*Conjugate[x4[t]]*x3[t]*Sin[\[Alpha]]) + x1[t], 
    x3'[t] == ((-I*(x3[
             t] (0.5 \[Omega]1 + 
              0.5 g Sqrt[10 x1[t]] Cos[x2[t]]*Cos[\[Alpha]]) + 
           0.5 x4[t] g Sqrt[10 x1[t]] Cos[x2[t]]*Sin[\[Alpha]]))/
       Sqrt[(Abs[x3[t]]^2 + Abs[x4[t]]^2)]), 
    x4'[t] == ((-I*(x4[
             t] (-0.5 \[Omega]1 - 
              0.5 g Sqrt[10 x1[t]] Cos[x2[t]]*Cos[\[Alpha]]) + 
           0.5 x3[t] g Sqrt[10 x1[t]] Cos[x2[t]]*Sin[\[Alpha]]))/
       Sqrt[(Abs[x3[t]]^2 + Abs[x4[t]]^2)]), x1[0] == N[\[Pi]/20], 
    x2[0] == 0, x3[0] == 0, x4[0] == 1}, {x1, x2, x3, x4}, {t, 0, 
    2 Pi}, Method -> "ExplicitEuler", StartingStepSize -> 0.0002, 
   MaxSteps -> 10^6];
Plot[Evaluate[Abs[{x1[t], x2[t], x3[t], x4[t]}] /. sol1x1xx[[1]]], {t,
   0.1, 2 Pi}, PlotLegends -> {x1, x2, x3, x4}, PlotRange -> All, 
 PlotLabel -> Row[{"K1 = ", K1, "g1 = ", g1}], AxesLabel -> Automatic,
  PlotRange -> All]

enter image description here

Improve this answer
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4
  • $\begingroup$ If we put g1=0 and g=1 then it occurs complex infinity why is it so. $\endgroup$
    – user68207
    May 19, 2021 at 8:01
  • $\begingroup$ I am using mathematica 11 and I am getting an error for g=0 case "Maximum number of 1000000 steps reached at the point t == \ 6.189534468092993". $\endgroup$
    – user68207
    May 19, 2021 at 8:06
  • $\begingroup$ Version: 12.0.0 for Linux x86 (64-bit) also gives the error "Maximum number of 1000000 steps reached at the point t == 6.1613966595956065`." $\endgroup$
    – user49048
    May 19, 2021 at 8:34
  • $\begingroup$ The solution for x1[t] diverges near t=1.1. A possible troublemaker is the term Sin[(1000 + 0.5)*(t - n)]/((2 Pi) Sin[(t - n x0)/2]) in the equation for x1. If t==n x0 it diverges. $\endgroup$
    – Daniel Huber
    May 19, 2021 at 8:35

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