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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

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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