wlferguson19

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1 years, 55 days
Just a student trying to learn maple.

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These are questions asked by wlferguson19

Hi everyone,

I'm a student studying pde's and I was trying to find a tool for me to understand it a lot better.

The heat equation is given by: Ut = a^2*Uxx

Take the example of a rod that is insulated at both ends (establishing BC's) of Ux(0,t) = 0 and Ux(L,t) = 0. Let's define the intial condition for any temperature at point x as x*(L-X).  We know that if we try to solve the steady-state solution, setting Ut = 0, we get Uxx = 0 which implies the general solution is U(x) = C1x + C2

From our boundary conditions we can see that a rod insulated at both ends -- and I should say laterally also -- should have a graph that turns from a quadratic to a horizontal line that is defined as the average of the initial conditon function from 0 to L.

 

In summary: Does maple have a feature to animate the function turning from a quadratic to a horizontal line? I think it would be beneficial in the long term for learning about BC's and visualizing them in my head after I play around with it.

How would one go about and solve a boundary value problems i.e.:

y'' + a* y = 0 under dirilecht boundary y(0) = 0 and y(L) = 0; I know this shouldn't yield a trivial solution

likewise if i wanted to do neuman or mixed conditions, how should i approach that? 

thanks

 

 

How would I turn this set into matrix form?

would it be possible to seperate the matrix form into:

v1e^(lamba*t) + v2e^(lambda2*t) .... + v^ne^(lambdan*t) where v1, v2, and vn are the eigenvectors and lamba1, lambda2, and lamban are their respective eigenvectors.

Solving_ODE.mw

 

Here is an example.  How would I solve this non-homogeneous system of ODEs

How would I solve a linear algebra differential equation with initial conditions.

 

For example, what if I had:

 

x'(t) = [1 2 ; 3 4] x(t) such that the ics: (0,1)

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