detools::charODESystem --
characteristic system of partial differential equation
Introductiondetools::charODESystem(ldf,s) determines
the characteristic system of the linear differential equation
ldf. The identifier s is used as independent
variable of this system.
Call(s)detools::charODESystem(ldf, s, <, init>)
Parametersldf |
- | the differential equation: an element of a domain
generated with the constructor
Dom::LinearDifferentialFunction. |
s |
- | the independent variable: an identifier. |
init |
- | the initial conditions: a list of equations. |
Returnsan object of the type ode.
Related
Functionsdetools::characteristics,
detools::charSolve
Detailsdetools::charODESystem only determines the
characteristic system of the given differential equation; it does not
attempt to solve it, i.e. to explicitly compute the characteristics. If
this is the goal, call directly the method detools::characteristics.
Example
1With the following input one can determine the characteristic system of the differential equation 2 diff(u,x)+diff(u,y)+3 diff(u,z)-2 u=0 using tau as independent variable of the arising ordinary differential equations.
>> LDF := Dom::LinearDifferentialFunction(
Vars = [[x, y, z], u], Rest = [Types = "Indep"]):
ldf := LDF( 2*u([x]) + u([y]) + 3*u([z]) - 2*u ):
detools::charODESystem(ldf, tau)
ode({diff(x(tau), tau) - 2, diff(y(tau), tau) - 1,
diff(z(tau), tau) - 3, - 2 u(tau) + diff(u(tau), tau)},
{u(tau), x(tau), y(tau), z(tau)})