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3

I do not fully understand what you want to do but try this: Needs["NDSolveFEM"] b = 1; {xMin, xMax} = {-5, 5}; {zMin, zMax} = {0, 20}; nRegion = ToNumericalRegion[Rectangle[{xMin, zMin}, {xMax, zMax}]]; \[CapitalGamma]pi = NeumannValue[0, z == 0]; \[CapitalGamma]pf = DirichletCondition[p[x, z] == 1, z == zMax]; \[CapitalGamma]si = NeumannValue[s[...

10

NDSolve-based Solution tend = 500; lb = -150; rb = -lb; m = 1/2; a = 1.01; rs[r_] = Integrate[1/(1 - (2*m)/Sqrt[r^2 + a^2]), r]; l = 1; V[r_] = (1 - (2 m)/Sqrt[r^2 + a^2]) (l (l + 1)/(r^2 + a^2)); Vs[r_] = V@InverseFunction[rs][r]; interVs = FunctionInterpolation[Vs[r], {r, lb, rb}] mol[n:_Integer|{_Integer..}, o_:"Pseudospectral"] := {"...

12

This problem can be solved with method of lines and with FDM as well. Using NDSolve we have m = 1/2; int = Integrate[1/(1 - (2*m)/Sqrt[r^2 + a^2]), r, Assumptions -> a > 0]; rs[x_] := int /. r -> x; a = 1.01; l = 1; r[x_] := InverseFunction[rs][x]; V[r_] := (1 - (2*m)/Sqrt[r^2 + a^2]) (l (l + 1)/(r^2 + a^2)); Vs[x_] := V@InverseFunction[rs][x]; ...

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