detools::charODESystem
--
characteristic system of partial differential equationdetools::charODESystem
(ldf,s)
determines
the characteristic system of the linear differential equation
ldf
. The identifier s
is used as independent
variable of this system.
detools::charODESystem(ldf, s, <, init>)
ldf |
- | 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. |
an object of the type ode
.
detools::characteristics
,
detools::charSolve
detools::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
.With 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)})