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detools::characteristics -- characteristics of partial differential equation

Introduction

detools::characteristics(ldf,s) determines the characteristics of the linear differential equation ldf. The identifier s is used as parameter for the curves.

Call(s)

detools::characteristics(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

a list of expressions representing the characteristics in parametric form.

Related Functions

detools::charODESystem, detools::charSolve

Details

Example 1

With the following input one can determine the characteristics of the differential equation 2 diff(u,x)+diff(u,y)+3 diff(u,z)-2 u=0.

>> LDF := Dom::LinearDifferentialFunction(
                Vars = [[x, y, z], u], Rest = [Types = "Indep"]):
   ldf := LDF( 2*u([x]) + u([y]) + 3*u([z]) - 2*u ):
   detools::characteristics(ldf, tau)
      {[z(tau) = C1 + 3 tau, x(tau) = C2 + 2 tau, y(tau) = C3 + tau,
      
         u(tau) = C4 exp(2 tau)]}

The result gives the characteristic curve in parametric form. The constants C1, C13, C14, C15 could be fixed by adding some initial condition. It is easy to see that the basis characteristics, i.e. the projection on the space of the independent variables x, y, z, is a straight line and that the solution grows exponentially on it.




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