# Question:Solving non-linear coupled initial value problem

## Question:Solving non-linear coupled initial value problem

Maple

I am trying to solve three non-linear coupled initial value problems. The equations are a bit complicated. The MAPLE code is

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with*plots

eq[1] := (1/6)*Ra*v(x)^3*((2*v(x)*w(x)^2*(v(x)^2/w(x)^2-3)*(diff(w(x), x))-6*w(x)^3*(1-v(x)/w(x))^2*(diff(v(x), x)))*A+v(x)^2*w(x)^2*(2*v(x)/w(x)-3)*(diff(w(x), x))-3*w(x)^4*(1-v(x)/w(x))^2*(diff(v(x), x)))/(w(x)^2*(w(x)+2*A)^2*(2*v(x)+3*B))+u(x)

eq[2] := (1/105)*(diff(u(x)^2*(v(x)^2+11*B*v(x)+39*B^2)/v(x), x))+(1/6)*Ra*Pr*v(x)*((3*v(x)*w(x)^2*(v(x)^2/w(x)^2-2)*(diff(w(x), x))-12*w(x)^3*(1-v(x)/w(x))^2*(diff(v(x), x)))*A+v(x)^2*w(x)^2*(3*v(x)/w(x)-4)*(diff(w(x), x))-6*w(x)^4*(1-v(x)/w(x))^2*(diff(v(x), x)))/(w(x)^2*(w(x)+2*A)^2)-Pr*u(x)/v(x)

eq[3] := (1/60)*(diff(u(x)*w(x)^2*(v(x)*w(x)^3-4*v(x)^2*w(x)^2+5*v(x)^3*w(x)+(2*w(x)^3-6*v(x)*w(x)^2+20*v(x)^3)*B)/(v(x)^4*(w(x)+2*A)), x))-2/(w(x)+2*A)

pars := {A = 1, B = 1, Pr = .7, Ra = 100}

for i to 3 do Eq[i] := subs(pars, eq[i]) end do

eqs := Eq[1], Eq[2], Eq[3]

ICs := u(0) = 0, v(0) = 0, w(0) = 0

vars := u(x), v(x), w(x)

sol := dsolve({ICs, eqs}, {vars}, type = numeric)

sol(.1)

MAPLE says:

`Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up`
`Is it possible to solve the problem in MAPLE? If yes, then how do I approach?`
`Thanks,`
`Subho`
` `
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