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

Posted 3 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 = 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.
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Posted 3 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 = 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 3 months ago
 Thank you so much, it really helps me.