SolvePDE
SolvePDE[
eqns
,
y
,
{
x
,
xmin
,
xmax
}
]
finds a numerical solution to the ordinary differential equations
eqns
for the function
y
with the independent variable
x
in the range
xmin
to
xmax
.
SolvePDE[
eqns
,
y
,
{
x
,
xmin
,
xmax
}
,
{
t
,
tmin
,
tmax
}
]
finds a numerical solution to the partial differential equations
eqns
.
SolvePDE[
eqns
,
{
,
,
...
}
,
{
x
,
xmin
,
xmax
}
]
finds numerical solutions for the functions
.
SolvePDE
gives results in terms of
InterpolatingFunction
objects.
SolvePDE[
eqns
,
y
[
x
],
{
x
,
xmin
,
xmax
}
]
gives solutions for
y
[
x
]
rather than for the function
y
itself.
SolvePDE
solves a wide range of ordinary differential equations, and some partial differential equations.
In ordinary differential equations, the functions
must depend only on the single variable
x
. In partial differential equations, they may depend on more than one variable.
The differential equations must contain enough initial or boundary conditions to determine the solutions for the
completely.
Initial and boundary conditions are typically stated in form
y
[
]
==
,
y
'[
]
==
, etc., but may consist of more complicated equations.
The point
that appears in the initial or boundary conditions need not lie in the range
xmin
to
xmax
over which the solution is sought.
The differential equations in
SolvePDE
can involve complex numbers.
See also:
D
,
Integrate
,
ND
,
NIntegrate
,
SolveEquation
.
Examples
Using InstantCalculators
Here are the InstantCalculators for the
SolvePDE
function. Enter the parameters for your calculation and click
Calculate
to see the result.
In[1]:=
Out[1]=
In[2]:=
Entering Commands Directly
You can paste a template for this command via the Text Input button on the
SolvePDE
Function Controller.
In[3]:=
Out[3]=
