Message Boards

WOLFRAM COMMUNITY

5267 Views

4 Replies

2 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Help solving system of 3 differential equations?

Diogo Carvalho

Posted 3 years ago

Basically, I want to solve a system of 3 differential equations. Here I am initializing some variables and defining f0 that is g(v,t=0). a = 0.5; b = (3^0.5)/2; ve = 1; u = 1; f0[v_] = (a/(Pi)^0.5)Exp[v^2/ve^2] + (b/(Pi)^0.5)Exp[(v - u)^2/ve^2]; u1 = Log[((1 - a^2)/a^2)^0.5]/(2u) + u/2; u2 = 3u/2 - Log[((1 - a^2)/a^2)^0.5]/(2u); f0[u1] f0[u2] Here I am using a system of 3 equations for 3 functions and equating g(v,0)=f0 sol = NDSolve[{ D[go[v, t], t] + D[D[w[v, t], t], v]/(v^3) + (-3v^(-4))D[w[v, t], t] == 0, g[v, t] == Pi/2 (v^2) D[go[v, t], v], go[v, 0] == f0[v], D[w[v, t], t] == 2g[v, t]*w[v, t], w[v, 0] == 0}, {go[v, t], W[v, t]}, {v, u1, u2}, {t, 0, 10000000000}]

Basically, I want to solve a system of 3 differential equations.

Here I am initializing some variables and defining f0 that is g(v,t=0).

a = 0.5;

b = (3^0.5)/2;

ve = 1;

u = 1;

f0[v_] = (a/(Pi)^0.5)*Exp[v^2/ve^2] + (b/(Pi)^0.5)*Exp[(v - u)^2/ve^2];

u1 = Log[((1 - a^2)/a^2)^0.5]/(2*u) + u/2;

u2 = 3*u/2 - Log[((1 - a^2)/a^2)^0.5]/(2*u);

f0[u1]

f0[u2]

Here I am using a system of 3 equations for 3 functions and equating g(v,0)=f0

sol = NDSolve[{ 

D[go[v, t], t] + 
D[D[w[v, t], t], v]/(v^3) + (-3*v^(-4))*D[w[v, t], t] == 0, 

g[v, t] == Pi/2 *(v^2) *D[go[v, t], v],

go[v, 0] == f0[v],

D[w[v, t], t] == 2*g[v, t]*w[v, t],

w[v, 0] == 0},

{go[v, t], W[v, t]},

{v, u1, u2},

{t, 0, 10000000000}]

POSTED BY: Diogo Carvalho

4 Replies

Sort By:

xzczd 　

Posted 3 years ago

Cross-posted: https://mathematica.stackexchange.com/q/261236/1871

POSTED BY: xzczd 　

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 3 years ago

Eliminate `g` and don't capitalize `w`: a = 1/2; b = Sqrt[3]/2; ve = 1; u = 1; f0[v_] = (a/Sqrt[Pi])Exp[v^2/ve^2] + (b/Sqrt[Pi])Exp[(v - u)^2/ve^2]; u1 = Log[((1 - a^2)/a^2)^(1/2)]/(2u) + u/2; u2 = 3u/2 - Log[((1 - a^2)/a^2)^(1/2)]/(2u); sol = NDSolve[{D[go[v, t], t] + D[D[w[v, t], t], v]/(v^3) + (-3v^(-4))D[w[v, t], t] == 0, go[v, 0] == f0[v], D[w[v, t], t] == 2Pi/2(v^2)D[go[v, t], v]*w[v, t], w[v, 0] == 0}, {go[v, t], w[v, t]}, {v, u1, u2}, {t, 0, 10000000000}]

Eliminate g and don't capitalize w:

a = 1/2; b = Sqrt[3]/2; ve = 1; u = 1;
f0[v_] = (a/Sqrt[Pi])*Exp[v^2/ve^2] +
   (b/Sqrt[Pi])*Exp[(v - u)^2/ve^2];
u1 = Log[((1 - a^2)/a^2)^(1/2)]/(2*u) + u/2;
u2 = 3*u/2 - Log[((1 - a^2)/a^2)^(1/2)]/(2*u); sol = 
 NDSolve[{D[go[v, t], t] + D[D[w[v, t], t], v]/(v^3) +
     (-3*v^(-4))*D[w[v, t], t] == 0,
   go[v, 0] == f0[v],
   D[w[v, t], t] == 2*Pi/2*(v^2)*D[go[v, t], v]*w[v, t],
   w[v, 0] == 0},
  {go[v, t], w[v, t]},
  {v, u1, u2}, {t, 0, 10000000000}]

POSTED BY: Gianluca Gorni