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Solve a Second-Order Differential Equation Numerically, with boundary conditions?

October 10, 2018   BI News and Info
 Solve a Second Order Differential Equation Numerically, with boundary conditions?

Below is an ODE with BC define as x[R]=0, x'[0]=0, x'[R]=0 and parameter n. The ODE is stiff at certain data, and I need to see the behavior of x’ and x for given parameters. I appreciate any help.

c = -0.7177;
r1 = 0.8;
r2 = 125;
R = 1.29;
f[r_] := Piecewise[{{0, 0 <= r <= r1}, {900/(1 - r1^3), 
    r1 < r <= 1}, {0, 1 < r <= R}}]


ps = ParametricNDSolveValue[{x''[r] + (1/r) x'[r] == 
    c n Exp[-x[r]] + f[r], x'[0] == 0, x[0] == x0}, {x, x'}, {r, 0, 
   R}, {x0,n}, Method -> "StiffnessSwitching"]

ff = FindRoot[{Last[ps[x0,n]][R] == 0, First[ps[x0,n]][R] == 0}, {x0, -2}]

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Recent Questions – Mathematica Stack Exchange

boundary, Conditions, differential, equation, Numerically, SecondOrder, solve
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