I have written this set of dynamic equations for my problem related to magnetized targets in fusion. I just want to know why Mathematica cannot solve it. I have done this "NDSolve" before and i have taken good answers. but when I change my formulas it cannot solve, what is the problem. I can sendyou the entire code.
`bal = {(3/2)*ne[t]*k*Te'[t] == \[Eta]d*wd + wie - wb +
f\[Alpha]*\[Eta]f*wf - whe, (3/2)*ni[t]*k*
Ti'[t] == (1 - \[Eta]d)*wd - wie + f\[Alpha]*(1 - \[Eta]f)*wf -
whi, nd'[t] = -nd[t]*nT[t]*\[Sigma],
nT'[t] = -nd[t]*nT[t]*\[Sigma],
n\[Alpha]'[t] = nd[t]*nT[t]*\[Sigma], Te[0] = 1, Ti[0] = 1,
nd[0] == nT[0] == \!\(TraditionalForm\`
\*FractionBox[\(1.4447999999999998`*^26\), \(2\)]\), n\[Alpha][0] = 0}
sol = NDSolve[bal, {Te, Ti, nd, nT, n\[Alpha]}, t]
here is the error.
NDSolve::deqn: Equation or list of equations expected instead of -
((2.85474*10^-12 E^(-19.983 ((1<<1>>Plus[<<3>>]<<1>>Power<<1>>
<<1>>])/Ti[t])^(1/3)) nd[t] nT[t])/(Ti[t]^(2/3) (1-(15.136 Ti[t]+4.6064
Ti[<<1>>]^2-0.10675 Ti[<<1>>]^3)/(1000+75.189 Ti[<<1>>]+13.5
Power[<<2>>]+0.01366 Power[<<2>>]))^(5/6))) in the first argument
{4.8*10^-9 nd[t] (Te^\[Prime])[t]==900000000000000000-8.70051*10^-25
(nd[t]+nT[t])^2 Sqrt[Te[t]]-(5.2266*10^46 <<1>>^<<1>> (11.92
+1.69505*10^-9 <<1>>^3))/((nd[t]+nT[t]) (3.77 +<<21>>
<<1>>+1.32084*10^-19 Power[<<2>>]))+(8.7331*10^17 (24-Log[Times[<<4>>]])
nd[t]^2 (-Te[t]+Ti[t]))/(1.09626*10^24 Te[<<1>>]+5.97059*10^20
<<1>>)^(3/2)+(5.152*10^-16 E^(-19.983 Times[<<2>>]^(1/3)) nd[t] nT[t]
(8/3 (4.32916*10^-7+Times[<<3>>])+64/9 Plus[<<2>>]^2))/((1+104/27
Plus[<<2>>]+64/9 Power[<<2>>]) (32+Te[t]) Ti[t]^(2/3) (1-Plus[<<3>>]
Power[<<2>>])^(5/6)),<<7>>,0}.`enter code here`
I change some = to == and I assign values to all the unknown variables and get rid of the TraditionalForm wrapper to turn that into an ordinary fraction
k=1;\[Eta]d=1;wd=1;wie=1;wb=1;f\[Alpha]=1;\[Eta]f=1;wf=1;whe=1;whi=1;\[Sigma]=1;
ne[t_]:=2t+1;ni[t_]:=3t+2;
bal = {(3/2)*ne[t]*k*Te'[t] == \[Eta]d*wd + wie - wb + f\[Alpha]*\[Eta]f*wf - whe,
(3/2)*ni[t]*k*Ti'[t] == (1 - \[Eta]d)*wd - wie + f\[Alpha]*(1 - \[Eta]f)*wf - whi,
nd'[t] == -nd[t]*nT[t]*\[Sigma],
nT'[t] == -nd[t]*nT[t]*\[Sigma],
n\[Alpha]'[t] == nd[t]*nT[t]*\[Sigma],
Te[0] == 1,
Ti[0] == 1,
nd[0] == nT[0] == 1.4447999999999998`*^26/2,
n\[Alpha][0] == 0};
sol = NDSolve[bal, {Te,Ti,nd,nT,n\[Alpha]}, {t,0,1}];
Plot[{Te[t],Ti[t]}/.sol[[1]],{t,0,1}]
Now substitute your actual values for all those variables and your actual functions for ne[t] and ni[t] and see what you get.