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Mathematica Calculus Equation Solving Wolfram Language

using the solutions of differential equations system

saysics saja

Posted 10 years ago

Hello,, I am trying to solve system of differential equations x,y and z depended on time t, with different values of constant c. where c= 2.2758, 2.04822, 1.82064, 1.59306, 1.36548 . then I want to use the solution of the differential equations system to plot equation F that depend on x[t] and plot equation FT that depend on y[t] and c So what i want is plot a variety of different graphs for F and FT over the range of c and if it possible to get each graphs with different color. Clear[t] \[Tau] = 13.8; \[Omega]0 = 1; r = 0.7071; n = 1.7758; \[HBar] = 1.0545717310^-34; \[Omega] = 0.5; k = 1666666.667; s = 2.2758; cVals = {2.2758, 2.04822, 1.82064, 1.59306, 1.36548} system1 = {x'[t] == ny[t], y'[t] == -nx[t] -cE^(-(r^2/\[Omega]0^2) ((t^2(1.177^2))/\[Tau]^2))z[t], z'[t] ==cE^(-(r^2/\[Omega]0^2) ((t^2(1.177^2))/\[Tau]^2))y[t]}; initialvalues1 = {x[-20] == 0, y[-20] == 0, z[-20] == 1}; sol1 = NDSolve[ Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t, -20, 20}]; F = (-10^33s\[HBar]rx[t])/\[Omega]0^2E^(-(r^2/\[Omega]0^2) ((t^2(1.177^2))/\[Tau]^2)); FT = (-10^33c\[HBar]ry[t])/\[Omega]0^2E^(-(r^2/\[Omega]0^2) ((t^2*(1.177^2))/\[Tau]^2)); P1 = Plot[Evaluate[F /. sol1], {t, -20, 20}, FrameLabel -> {t, F}, Frame -> True, FrameTicks -> All] P2 = Plot[Evaluate[FT /. sol1], {t, -20, 20}, FrameLabel -> {t, FT}, Frame -> True, FrameTicks -> All] that did not work,so I trying use ParametricNDSolveValue pfun = ParametricNDSolveValue[Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t,-20, 20}, {c}]; but I didn't know how to use pfun in F and FT equations Thanks,

Hello,,

I am trying to solve system of differential equations x,y and z depended on time t, with different values of constant c. where c= 2.2758, 2.04822, 1.82064, 1.59306, 1.36548 .

then I want to use the solution of the differential equations system to plot equation F that depend on x[t]

and plot equation FT that depend on y[t] and c

So what i want is plot a variety of different graphs for F and FT over the range of c and if it possible to get each graphs with different color.

     Clear[t]
    \[Tau] = 13.8;
    \[Omega]0 = 1;
    r = 0.7071;
    n = 1.7758;
    \[HBar] = 1.05457173*10^-34;
    \[Omega] = 0.5;
    k = 1666666.667;
    s = 2.2758;
    cVals = {2.2758, 2.04822, 1.82064, 1.59306, 1.36548}

    system1 = {x'[t] == n*y[t],
       y'[t] == -n*x[t] -c*E^(-(r^2/\[Omega]0^2)  ((t^2*(1.177^2))/\[Tau]^2))*z[t],
       z'[t] ==c*E^(-(r^2/\[Omega]0^2)  ((t^2*(1.177^2))/\[Tau]^2))*y[t]};
    initialvalues1 = {x[-20] ==  0, y[-20] ==  0, z[-20] ==   1};
    sol1 = NDSolve[ Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t, -20, 20}];
    F = (-10^33*s*\[HBar]*r*x[t])/\[Omega]0^2*E^(-(r^2/\[Omega]0^2)  ((t^2*(1.177^2))/\[Tau]^2));

    FT = (-10^33*c*\[HBar]*r*y[t])/\[Omega]0^2*E^(-(r^2/\[Omega]0^2)  ((t^2*(1.177^2))/\[Tau]^2));

    P1 = Plot[Evaluate[F /. sol1], {t, -20, 20}, FrameLabel -> {t, F}, Frame -> True, FrameTicks -> All]
    P2 = Plot[Evaluate[FT /. sol1], {t, -20, 20}, FrameLabel -> {t, FT}, Frame -> True, FrameTicks -> All]

that did not work,so I trying use ParametricNDSolveValue

pfun = ParametricNDSolveValue[Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t,-20, 20}, {c}];

but I didn't know how to use pfun in F and FT equations

Thanks,

POSTED BY: saysics saja

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saysics saja

Posted 10 years ago

Works great, thanks alot!

POSTED BY: saysics saja

Anderson Coser Gaudio

Anderson Coser Gaudio, Federal University of Espirito Santo

Posted 10 years ago

Hi, I'm sorry for the already used "n". I hope the code below be more useful for you. Clear[t] \[Tau] = 13.8; \[Omega]0 = 1; r = 0.7071; n = 1.7758; \[HBar] = 1.0545717310^-34; \[Omega] = 0.5; k = 1666666.667; s = 2.2758; cVals = {2.2758, 2.04822, 1.82064, 1.59306, 1.36548}; ( Define colors for the plots ) color = {Red, Yellow, Green, Cyan, Blue}; Do[ c = cVals[[i]]; ( cVals[[i]] is the i^th value of cVals list ) system1 = {x'[t] == ny[t], y'[t] == -nx[t] - cE^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2))z[t], z'[t] == cE^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2))y[t]}; initialvalues1 = {x[-20] == 0, y[-20] == 0, z[-20] == -1}; sol1 = NDSolve[ Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t, -20, 20}]; F = (-10^33s\[HBar]rx[t])/\[Omega]0^2 E^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2)); FT = (-10^33c\[HBar]ry[t])/\[Omega]0^2 E^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2)); ( Build and store graphics in the appropriate list ) Subscript[plotF, i] = Plot[Evaluate[F /. sol1], {t, -20, 20}, FrameLabel -> {"t", "F"}, Frame -> True, FrameTicks -> All, PlotStyle -> color[[i]]]; Subscript[plotFT, i] = Plot[Evaluate[FT /. sol1], {t, -20, 20}, FrameLabel -> {"t", "FT"}, Frame -> True, FrameTicks -> All, PlotStyle -> color[[i]]]; , {i, Length[cVals]}] ( Iterate through the c values *) Show[{Subscript[plotF, 1], Subscript[plotF, 2], Subscript[plotF, 3], Subscript[plotF, 4], Subscript[plotF, 5]}] Show[{Subscript[plotFT, 1], Subscript[plotFT, 2], Subscript[plotFT, 3], Subscript[plotFT, 4], Subscript[plotFT, 5]}]

Hi,

I'm sorry for the already used "n". I hope the code below be more useful for you.

Clear[t]

\[Tau] = 13.8;
\[Omega]0 = 1;
r = 0.7071;
n = 1.7758;
\[HBar] = 1.05457173*10^-34;
\[Omega] = 0.5;
k = 1666666.667;
s = 2.2758;
cVals = {2.2758, 2.04822, 1.82064, 1.59306, 1.36548};

(* Define colors for the plots *)
color = {Red, Yellow, Green, Cyan, Blue};

Do[
 c = cVals[[i]]; (* cVals[[i]] is the i^th value of cVals list *)

 system1 = {x'[t] == n*y[t], 
   y'[t] == -n*x[t] - 
     c*E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2))*z[t], 
   z'[t] == 
    c*E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2))*y[t]};

 initialvalues1 = {x[-20] == 0, y[-20] == 0, z[-20] == -1};

 sol1 = NDSolve[
   Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t, -20, 20}];

 F = (-10^33*s*\[HBar]*r*x[t])/\[Omega]0^2*
   E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2));
 FT = (-10^33*c*\[HBar]*r*y[t])/\[Omega]0^2*
   E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2));

 (* Build and store graphics in the appropriate list *)
 Subscript[plotF, i] = 
  Plot[Evaluate[F /. sol1], {t, -20, 20}, FrameLabel -> {"t", "F"}, 
   Frame -> True, FrameTicks -> All, PlotStyle -> color[[i]]];
 Subscript[plotFT, i] = 
  Plot[Evaluate[FT /. sol1], {t, -20, 20}, FrameLabel -> {"t", "FT"}, 
   Frame -> True, FrameTicks -> All, PlotStyle -> color[[i]]];

 , {i, Length[cVals]}] (* Iterate through the c values *)

Show[{Subscript[plotF, 1], Subscript[plotF, 2], Subscript[plotF, 3], 
  Subscript[plotF, 4], Subscript[plotF, 5]}]
Show[{Subscript[plotFT, 1], Subscript[plotFT, 2], Subscript[plotFT, 
  3], Subscript[plotFT, 4], Subscript[plotFT, 5]}]

POSTED BY: Anderson Coser Gaudio

saysics saja

Posted 10 years ago

Thanks, it's work But I have some question what do you mean by c = cVals[[n]] ? is n here the same constant I had in the equation ? I am afraid that code will multiply n*c also how I put all the curves of F together in the same figure with different color(I don't want them in table)? I want to do the same for FT also

POSTED BY: saysics saja

Anderson Coser Gaudio

Anderson Coser Gaudio, Federal University of Espirito Santo

Posted 10 years ago

Hi, See if this makes sense to you. Clear[t] \[Tau] = 13.8; \[Omega]0 = 1; r = 0.7071; n = 1.7758; \[HBar] = 1.0545717310^-34; \[Omega] = 0.5; k = 1666666.667; s = 2.2758; cVals = {2.2758, 2.04822, 1.82064, 1.59306, 1.36548}; plotF = {}; plotFT = {}; Do[ c = cVals[[n]]; system1 = {x'[t] == ny[t], y'[t] == -nx[t] - cE^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2))z[t], z'[t] == cE^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2))y[t]}; initialvalues1 = {x[-20] == 0, y[-20] == 0, z[-20] == -1}; sol1 = NDSolve[ Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t, -20, 20}]; F = (-10^33s\[HBar]rx[t])/\[Omega]0^2 E^(-(r^2/\[Omega]0^2) - ((t^2(1.177^2))/\[Tau]^2)); FT = (-10^33c\[HBar]ry[t])/\[Omega]0^2 E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2)); plotF = Append[plotF, Plot[Evaluate[F /. sol1], {t, -20, 20}, FrameLabel -> {"t", "F"}, Frame -> True, FrameTicks -> All]]; plotFT = Append[plotFT, Plot[Evaluate[FT /. sol1], {t, -20, 20}, FrameLabel -> {"t", "FT"}, Frame -> True, FrameTicks -> All]]; , {n, Length[cVals]}] Table[{plotF[[n]], plotFT[[n]]}, {n, Length[cVals]}]

Hi,

See if this makes sense to you.

Clear[t]
\[Tau] = 13.8;
\[Omega]0 = 1;
r = 0.7071;
n = 1.7758;
\[HBar] = 1.05457173*10^-34;
\[Omega] = 0.5;
k = 1666666.667;
s = 2.2758;
cVals = {2.2758, 2.04822, 1.82064, 1.59306, 1.36548};
plotF = {};
plotFT = {};

Do[
 c = cVals[[n]];
 system1 = {x'[t] == n*y[t], 
   y'[t] == -n*x[t] - 
     c*E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2))*z[t], 
   z'[t] == 
    c*E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2))*y[t]};
 initialvalues1 = {x[-20] == 0, y[-20] == 0, z[-20] == -1};
 sol1 = NDSolve[
   Join[system1, initialvalues1], {x[t], y[t], z[t]}, {t, -20, 20}];

 F = (-10^33*s*\[HBar]*r*x[t])/\[Omega]0^2*
   E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2));

 FT = (-10^33*c*\[HBar]*r*y[t])/\[Omega]0^2*
   E^(-(r^2/\[Omega]0^2) - ((t^2*(1.177^2))/\[Tau]^2));

 plotF = Append[plotF, 
   Plot[Evaluate[F /. sol1], {t, -20, 20}, FrameLabel -> {"t", "F"}, 
    Frame -> True, FrameTicks -> All]];
 plotFT = 
  Append[plotFT, 
   Plot[Evaluate[FT /. sol1], {t, -20, 20}, FrameLabel -> {"t", "FT"},
     Frame -> True, FrameTicks -> All]];
 , {n, Length[cVals]}]

Table[{plotF[[n]], plotFT[[n]]}, {n, Length[cVals]}]

POSTED BY: Anderson Coser Gaudio

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