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Question: unable to convert to an explicit first-order system

Question:unable to convert to an explicit first-order system

Madhukesh J K 140 Maple 17
ode dsolve numeric differential-equations bvp
November 11 2021
1

Hi

I got the error like this unable to convert to an explicit first-order system

please anyone can help me to solve this

I am attaching the worksheet

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with(plots); restart
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eq1 := (2*eta*gamma+1)*(diff(f(eta), `$`(eta, 3)))+2*gamma*(diff(f(eta), `$`(eta, 2)))+f(eta)*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0;

(2*eta*gamma+1)*(diff(diff(diff(f(eta), eta), eta), eta))+2*gamma*(diff(diff(f(eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0

 (1)
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eq2 := (diff(F(eta), `$`(eta, 2)))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0;

(diff(diff(F(eta), eta), eta))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0

 (2)
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eq3 := (2*eta*gamma+1)*(1+Rd)*(diff(theta(eta), `$`(eta, 2)))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0;

(2*eta*gamma+1)*(1+Rd)*(diff(diff(theta(eta), eta), eta))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0

 (3)
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eq4 := 2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0;

2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0

 (4)
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bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0

 (5)
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params := [Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1];

[Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1]

 (6)
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sol := dsolve(eval([eq1, eq2, eq3, eq4, bcs], params), numeric, output = array([0]), maxmesh = 5000, initmesh = 1000)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

  
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