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Error solving nonlinear coupled ODE: ndnum: Encountered non-numerical value for a derivative

Muhammad Usman

Muhammad Usman, XJTU

Posted 2 months ago

I am trying to solve the coupled non linear ODEs using ParametricNDSolveValue and it is not generating the results. Here is the code: We = 0.4; alpha = 0.9; beta = 0.2; phi = 0.7; P = -1.3; Br = 0.1; K1 = We^2(1 - alpha^2); K2 = phiK1; system = {{u''[y] + 3((phi - 1)/(phi + 1))We^2(1 - alpha^2) (u'[y])^2u''[y] - 5((phi - 1)/(phi + 1))We^4(1 - alpha^2)^2 (u'[y])^4 u''[y] - (1/(phi + 1))P(1 + beta . t[y]) == 0, t''[y] + Br(1 - beta . t[y])((u'[y])^2 - K1(u'[y])^4 + K2(u'[y])^4 - K1K2(u'[y])^6) == 0, u[0] == 1, u[1] == c, t[0] == 0, t[1] == c}} sols = ParametricNDSolveValue[system, {u, t}, {y, 0, 1}, {c}] Plot[Evaluate[Table[sols[c][y], {c, -1, 1, 0.1}]], {y, 0, 1}, PlotRange -> All] I am now getting the error. "ParametricNDSolveValue::ndnum: Encountered non-numerical value for a derivative at y$17528 == 0.`." Please help me to generate the results.

I am trying to solve the coupled non linear ODEs using ParametricNDSolveValue and it is not generating the results. Here is the code:

We = 0.4; alpha = 0.9; beta = 0.2; phi = 0.7; P = -1.3; Br = 0.1; K1 = We^2*(1 - alpha^2); K2 = phi*K1;
system = {{u''[y] + 
     3*((phi - 1)/(phi + 1))*We^2*(1 - alpha^2) (u'[y])^2*u''[y] - 
     5*((phi - 1)/(phi + 1))*We^4*(1 - alpha^2)^2 (u'[y])^4*
      u''[y] - (1/(phi + 1))*P*(1 + beta . t[y]) == 0, 
   t''[y] + 
     Br*(1 - beta . t[y])*((u'[y])^2 - K1*(u'[y])^4 + K2*(u'[y])^4 - 
        K1*K2*(u'[y])^6) == 0, u[0] == 1, u[1] == c, t[0] == 0, 
   t[1] == c}}
sols = ParametricNDSolveValue[system, {u, t}, {y, 0, 1}, {c}]
Plot[Evaluate[Table[sols[c][y], {c, -1, 1, 0.1}]], {y, 0, 1}, 
 PlotRange -> All]

I am now getting the error. "ParametricNDSolveValue::ndnum: Encountered non-numerical value for a derivative at y$17528 == 0.`." Please help me to generate the results.

POSTED BY: Muhammad Usman

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Sangdon Lee

Posted 2 months ago

Several typing errors are removed. I used the ParametricNDSolve, rather than ParametricNDSolveValue. We = 0.4; alpha = 0.9; beta = 0.2; phi = 0.7; P = -1.3; Br = 0.1; K1 = We^2(1 - alpha^2); K2 = phiK1; system = { u''[y] + 3((phi - 1)/(phi + 1))We^2(1 - alpha^2)(u'[y])^2u''[y] - 5((phi - 1)/(phi + 1))We^4(1 - alpha^2)^2* (u'[y])^4* u''[y] - (1/(phi + 1))P(1 + betat[y]) == 0, t''[y] + Br(1 - betat[y])((u'[y])^2 - K1(u'[y])^4 + K2(u'[y])^4 - K1K2(u'[y])^6) == 0, u[0] == 1, u[1] == c, t[0] == 0, t[1] == c } sols = ParametricNDSolve[system, {u, t}, {y, 0, 1}, {c}] Plot[Evaluate[Table[u[c][y] /. sols, {c, -1, 1, 0.1}]], {y, 0, 1}, PlotRange -> All]

Several typing errors are removed. I used the ParametricNDSolve, rather than ParametricNDSolveValue.

We = 0.4; alpha = 0.9; beta = 0.2; phi = 0.7; P = -1.3; Br = 0.1; K1 =
  We^2*(1 - alpha^2); K2 = phi*K1;

system = {
  u''[y] + 
    3*((phi - 1)/(phi + 1))*We^2*(1 - alpha^2)*(u'[y])^2*u''[y] - 
    5*((phi - 1)/(phi + 1))*We^4*(1 - alpha^2)^2* (u'[y])^4*
     u''[y] - (1/(phi + 1))*P*(1 + beta*t[y]) == 0,

  t''[y] + 
    Br*(1 - beta*t[y])*((u'[y])^2 - K1*(u'[y])^4 + K2*(u'[y])^4 - 
       K1*K2*(u'[y])^6) == 0,

  u[0] == 1, u[1] == c, t[0] == 0, t[1] == c
  }

sols = ParametricNDSolve[system, {u, t}, {y, 0, 1}, {c}] 

Plot[Evaluate[Table[u[c][y] /. sols, {c, -1, 1, 0.1}]], {y, 0, 1}, 
 PlotRange -> All]

POSTED BY: Sangdon Lee

Muhammad Usman

Muhammad Usman, XJTU

Posted 2 months ago

Thank you so much, it really helps me.

POSTED BY: Muhammad Usman

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