## `detools::charODESystem` -- characteristic system of partial differential equation

#### Introduction

`detools::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>)`

#### Parameters

`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.

#### Returns

an object of the type `ode`.

#### Related Functions

`detools::characteristics`, `detools::charSolve`

#### Details

- `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`.
- The implemented form of the method of characteristics works only for (quasi-)linear first order equations in one dependent variable.
- With the optional third argument one can prescribe some initial conditions for the characteristic system. There should be exactly one condition for each independent and dependent variable of the original partial differential equation.

#### Example 1

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)})

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