Hello physicists,(adsbygoogle = window.adsbygoogle || []).push({});

Pretty new to Mathematica here. I'm looking to verify that $$P(s,\tilde{t}|_{s_0}) = 2\tilde{b}_{\rho} \frac{s^{\alpha+1}}{\check{s_0}^{\alpha}}I_{\alpha}(2\tilde{b}_{\rho}s\check{s}_0)exp[-\tilde{b}_{\rho}(s^2+\check{s_0}^2)]$$

Is a solution to

$$\frac{\partial}{\partial{\tilde{t}}}P(s, \tilde{t}) = \frac{\partial}{\partial s}[(2b_{\rho}s - \frac{\rho}{s})P(s,\tilde{t})] + \frac{\partial^2}{\partial s^2}[P(s,\tilde{t})]$$

Where $$\alpha = \frac{\rho - 1}{2}$$ $$\tilde{b}_{\rho} = \frac{b_{\rho}}{1-e^{-\tilde{t}}}$$ $$\check{s}_0 = s_0 exp(\frac{-\tilde{t}}{2})$$ and $$I_{\alpha}$$ is a modified Bessel function of the first kind.

Following with this link, I wrote the following into Mathematica:

First I defined the variables in the solution as given above:

a = (r - 1)/2

b = b1/(1 - Exp[-t])

s0 = s01*Exp[-t/2]

i = BesselI[a, 2*b*s*s0]

I entered the solution like such:

q[s, t] = 2 b s^(a + 1)/(s0)*i*Exp[-b (s^2 + s0^2)]

I entered the general form of the equation:

E3 = D[p[s, t], t] == D[(2 b1 s - r/s) p[s, t], s] + D[p[s, t], {s, 2}]

Now I'm looking to "replace" the proposed solution q into E3 as p[s,t] and hope to get {True} as the output:

Simplify[E3 /. q[s, t]]

But the output is says: "___[contents of q]__ is neither a list of replacement rules nor a valid dispatch table and so cannot be used for replacing."

So I must be assigning something incorrectly... Does you see something wrong with this or know of an easier way to verify PDE solutions using Mathematica?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mathematica Verifying PDE solutions using Mathematica

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**