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# Help solving system of 3 differential equations?

Posted 2 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]/(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}] 
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Posted 2 years ago
 Cross-posted: https://mathematica.stackexchange.com/q/261236/1871
Posted 2 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)]/(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 2 years ago
 You should list all three unknown functions that you wish to calculate.
Posted 2 years ago
 dw(v,t)/dt =2g(v,t) w(t,v) g(t,v)= Pi/2 *(v^2)*d g0(v,t)/dt d go(v,t)/dt + d/dv[dw/dt *1/v^3)]=0 initial conditions f0=go(v,0) w(v,0)=0