CODEWITHSUNDEEP
juliasymbolic-mathcalculusdifferentiation
Alex
Alex

Reputation: 1

Is there any method in Julia to derive some equations with derivatives of functions at certain points(but without expressions)

New to Julia.I am trying to do some derivations by Symbolics.jl. I have a function which is defined as the sum of another two functions with expressions unassigned. As you can see, it's actually the d'Alembert solution of the wave equation.

using Symbolics, SymbolicUtils
@variables f(..) g(..) t x c
u = f(t-x/c) + g(t+x/c)

And I tried to use Dx = Differential(x) to represent the partial differentiation with respect to x. What I want to achieve is to give a certain boundary condition at x=0.

u'(0,t) = d/dx(f(t)+g(t)).

Dx = Differential(x)
dxu = expand_derivatives(Dx(u))
substitute(Dx(u), Dict([x => 0]))

Therefore, I can repeat similar procedures and get some equations(maybe I will subsititute f,g with some certain expressions later for analytical results).

However, Shown below is the output.

d/0 (f(t)+g(t))

Differential(0)(g(t) + f(t))

The desirable output may be：

d/dx (f(t)+g(t))

Differential(x)(g(t) + f(t))

So is there any method to do this in Julia? Do I simply need to use another Pkg or what?

Sorry for no images. Any advice will be appreciated.

Upvotes: 0

Views: 53

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