| Package | Description |
|---|---|
| dev.nm.analysis.differentialequation.pde.finitedifference.elliptic.dim2 | |
| dev.nm.analysis.differentialequation.pde.finitedifference.hyperbolic.dim1 | |
| dev.nm.analysis.differentialequation.pde.finitedifference.hyperbolic.dim2 | |
| dev.nm.analysis.differentialequation.pde.finitedifference.parabolic.dim1.convectiondiffusionequation | |
| dev.nm.analysis.differentialequation.pde.finitedifference.parabolic.dim1.heatequation |
One-dimensional heat/diffusion problems with explicit initial and boundary data.
|
| dev.nm.analysis.differentialequation.pde.finitedifference.parabolic.dim2 |
| Modifier and Type | Class and Description |
|---|---|
class |
PoissonEquation2D
Poisson's equation is an elliptic PDE that takes the following general form.
\[
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = f(x, y)
\]
with Dirichlet boundary conditions:
\[
u(0, y) = g(0, y) \\
u(a, y) = g(a, y) \\
u(x, 0) = g(x, 0) \\
u(x, b) = g(x, b)
\]
assuming that the domain of the independent variables is a rectangular region in the x-y plane.
|
| Modifier and Type | Class and Description |
|---|---|
class |
WaveEquation1D
A one-dimensional wave equation is a hyperbolic PDE that takes the following form.
\[
\frac{\partial^2 u}{\partial t^2} = \beta \frac{\partial^2 u}{\partial x^2}
\]
with both boundary ends fixed at 0, that is,
\[
u(t, 0) = u(t, a) = 0
\]
and two initial conditions, namely u and its first time derivative \(u_{t}\):
\[
u(0, x) = f(x), 0 < x < a \\
u_t(0, x) = g(x), 0 < x < a
\]
|
| Modifier and Type | Class and Description |
|---|---|
class |
WaveEquation2D
A two-dimensional wave equation is a hyperbolic PDE that takes the following form.
\[
\frac{\partial^2 u}{\partial t^2}
= \beta (\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2})
\]
with fixed boundary condition, that is,
\[
u(t, 0, 0) = u(t, a, 0) = u(t, 0, b) = u(t, a, b) = 0
\]
and two initial conditions, namely \(u\) and its first time derivative \(u_t\):
\[
u(0, x, y) = f(x, y), 0 < x < a, 0 < y < b \\
u_t(0, x, y) = g(x, y), 0 < x < a, 0 < y < b
\]
|
| Modifier and Type | Class and Description |
|---|---|
class |
ConvectionDiffusionEquation1D
The convection–diffusion equation is a combination of the diffusion and
convection (advection) equations, and describes physical phenomena where
particles, energy, or other physical quantities are transferred inside a
physical system due to two processes: diffusion and convection.
|
| Modifier and Type | Class and Description |
|---|---|
class |
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 \(0 \leq c_k \leq 1, k = 1, 2\).
|
| Modifier and Type | Class and Description |
|---|---|
class |
HeatEquation2D
A two-dimensional heat equation (or diffusion equation) is a parabolic PDE that takes the
following form.
\[
\frac{\partial u}{\partial t}
= \beta (\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}),
\]
with an initial condition of the form:
\[
u(0, x, y) = f(x, y), 0 < x < a, 0 < y < b
\]
and Dirichlet boundary conditions of the form:
\[
u(t, x, y) = g(t, x, y), (x, y) \in \delta R,
\]
where \(\delta R\) is the boundary of the surface R.
|
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