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# How can I use NDSolve for parametric functions ?

Posted 9 years ago
 Hello, I am trying to solve partial differential equation of parametric functions, but I think that NDSolve does not recognize the parametric function. Maybe I am wrong in defining the parametric function before solving differential equations. How can I fix this problem, could you help me ? In the following code, I wanted to make that d[t] is function of t (time). Thank you in advance. Have a nice day. R1 = 5.0; n = 9; dst = 19.26 10^3; mAu = dst (4[Pi])/3 (R1 10^-9)^3; eV = 1.6 10^-19; AAu = 3.0; ANi = 2.0; AVac = 0; A = (AAu^0.5 - AVac^0.5) (ANi^0.5 - AVac^0.5); \[Sigma]Au = 0.332; \[Sigma]Ni = 0.326; \[Sigma]tot = (((\[Sigma]Au)^6 + (\[Sigma]Ni)^6)/2)^(1/6); HvdW[d, t] = -(A/6) (1/(d[t]/R1) + 1/(2 + d[t]/R1) + Log[(d[t]/R1)/(2 + d[t]/R1)]); HBorn[d, t, B_] = 4 A (B)^(n - 6) 1/(n - 2)! ((6 - 2 d[t]/R1)/(2 + d[t]/R1)^(n - 5) + (6 - 2 d[t]/R1)/(d[t]/R1)^(n - 5)); En[d, t, B_] := HvdW[d, t] + HBorn[d, t, B]; Utot[d, t, B_] = eV 10^-15 En[d, t, B]; NDSolve[mAu 10^15 D[d[t], t, t] + 10^-3 (D[Utot[d, t, B], d[t]] /. B -> \[Sigma]tot/R1) == 0, (d[t] /. t -> 0) == -0.05, (D[d[t], t] /. t -> 0) == 0, d, {t, 0, 100}, MaxSteps -> Infinity]