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partial differential equation
- Thread starter jav_dec80
- Start date
Is your goal to solve this analytically on paper or are you able to use numerical methods such as finite difference in MATLAB?
Tidying things up, is this what you're given?
0 < x < 2 & t > 0
\(
\frac{\partial u}{\partial t} = 3\frac{\partial^{2} u}{\partial x^{2}}
\)
\(
\frac{\partial u}{\partial x}(0, t) = \frac{\partial u}{\partial x}(2, t) = 0
\)
\(
u(x, 0) = 3x
\)
Post the work that you have done to try and solve this. We can go from there.
ramueller11
- Joined Dec 13, 2013
- 4
The PDE is a well-known PDE: the heat equation or the diffusion equation. There most common solution and can be derived assuming the solution u(x,t) = X(x)T(t). The the other analytical solution involves the complementary error function. I suspect it involves Laplace/Fourier Transforms. However, the latter solution holds only for boundary conditions of 0 at x = +- infinity and intial conditions of a delta function. So this probably leaves the former as the likely solution which you will find is a Fourier series involving only cos(x) functions due to the boundary condition.
See this: http://en.wikipedia.org/wiki/Parabolic_partial_differential_equation
See this: http://en.wikipedia.org/wiki/Parabolic_partial_differential_equation
