| Package | Description |
|---|---|
| dev.nm.analysis.differentialequation.pde.finitedifference.parabolic.dim1.heatequation |
One-dimensional heat/diffusion problems with explicit initial and boundary data.
|
| Class and Description |
|---|
| HeatEquation1D
A one-dimensional heat equation (or diffusion equation) is a parabolic PDE that takes the
following form.
\[
\frac{\partial u}{\partial t} = \beta \frac{\partial^2 u}{\partial x^2},
\]
The initial condition has this form:
\[
u(0,x) = f(x), 0 < x < a
\]
The mixed boundary conditions have this form:
\[
(1-c_1)u(t,0) - c_1\frac{\partial u}{\partial x}(t,0) = g_1(t), \\
(1-c_2)u(t,a) + c_2\frac{\partial u}{\partial x}(t,a) = g_2(t)
\]
where \(0 \leq c_k \leq 1, k = 1, 2\).
|
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