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Question: Error, (in dsolve/numeric/bvp) singularity encountered

Question:Error, (in dsolve/numeric/bvp) singularity encountered

faisal 15 Maple
ode singular dsolve numeric differential-equations bvp
December 18 2017
0


 

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NULL
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restart
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with(plots)
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Pr := 0.1e-1

0.1e-1

 (1)
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Eq1 := (101-100*d)*(diff(h(eta), eta))+2*f(eta) = 0; Eq2 := (101-100*d)*(diff(f(eta), `$`(eta, 2)))-h(eta)*(diff(f(eta), eta))-f(eta)^2+g(eta)^2-beta*(f(eta)+(1/2)*eta*(diff(f(eta), eta))) = 0; Eq3 := diff(g(eta), `$`(eta, 2))-h(eta)*(diff(g(eta), eta))-2*f(eta)*g(eta)-beta*(g(eta)+(1/2)*eta*(diff(g(eta), eta))) = 0; Eq4 := diff(p(eta), eta)-2*(diff(f(eta), eta))+beta*(h(eta)+eta*(diff(h(eta), eta))) = 0; Eq5 := diff(theta(eta), `$`(eta, 2))-Pr*h(eta)*(diff(theta(eta), eta))-Pr*beta*(3*theta(eta)+eta*(diff(theta(eta), eta))) = 0

(101-100*d)*(diff(h(eta), eta))+2*f(eta) = 0

  

(101-100*d)*(diff(diff(f(eta), eta), eta))-h(eta)*(diff(f(eta), eta))-f(eta)^2+g(eta)^2-beta*(f(eta)+(1/2)*eta*(diff(f(eta), eta))) = 0

  

diff(diff(g(eta), eta), eta)-h(eta)*(diff(g(eta), eta))-2*f(eta)*g(eta)-beta*(g(eta)+(1/2)*eta*(diff(g(eta), eta))) = 0

  

diff(p(eta), eta)-2*(diff(f(eta), eta))+beta*(h(eta)+eta*(diff(h(eta), eta))) = 0

  

diff(diff(theta(eta), eta), eta)-0.1e-1*h(eta)*(diff(theta(eta), eta))-0.1e-1*beta*(3*theta(eta)+eta*(diff(theta(eta), eta))) = 0

 (2)
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NULL
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NULL
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`Vλ` := [.5, 1, 1.5]; `Vβ` := [0.5e-1, .1, .2, .4, .7, 1, 1.50, 2]
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etainf := 1
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bcs := h(0) = 0, p(0) = 0, theta(0) = 1, (D(f))(0) = lambda*f(0)^(4/3)/(f(0)^2+(1-g(0))^2)^(1/3), (D(g))(0) = -lambda*f(0)^(1/3)*(1-g(0)).(1/(f(0)^2+(1-g(0))^2)^(1/3)), f(etainf) = 0, g(etainf) = 0, theta(etainf) = 0

h(0) = 0, p(0) = 0, theta(0) = 1, (D(f))(0) = lambda*f(0)^(4/3)/(f(0)^2+(1-g(0))^2)^(1/3), (D(g))(0) = -f(0)^(1/3)*(1-g(0))*lambda/(f(0)^2+(1-g(0))^2)^(1/3), f(1) = 0, g(1) = 0, theta(1) = 0

 (3)
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NULL
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dsys := {Eq1, Eq2, Eq3, Eq4, Eq5, bcs}
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for j to 3 do for i to 8 do lambda := `Vλ`[j]; beta := `Vβ`[i]; dsol[j][i] := dsolve(dsys, numeric, continuation = d); print(beta); print(lambda); print(dsol[j][i](0)) end do end do

Error, (in dsolve/numeric/bvp) singularity encountered

  
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NULL
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NULL
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NULL


 

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