How can I obtain the differential transform(DTM) of ln(1+aT(x))?

Mohamed el Ibrahimi @Mohamed_El_Ibrahimi

09 September 2018 1 9K Report

I want solve the heat equation the temperature dependant materials, by using Differential Transform Method (DTM). I need transform ln(1+ a T(x)).

a: is a constant, x: is the variable and T: is the function.

Abayomi Samuel Oke

Several attempts were made to obtain the differential transform of transcendental function of dependent variables but I am yet to get a satisfactory answer.

For the meanwhile, you may want to consider approximating the function by a Taylor expansion, for instance,

Ln(1+aT(x)) = aT - (aT)^2/2 + (aT)^3/3 + ...

and then obtain the DTM of T, T^2, T^3,...

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