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detools::charSolve -- solves partial differential equation with the method of characteristics

Introduction

detools::charSolve(ldf,init,pars) solves the linear differential equation ldf by the method of characteristics. The initial conditions init should depend on n-1 parameters (listed in pars), if there are n independent variables.

Call(s)

detools::charSolve(ldf, init, pars)

Parameters

ldf - the differential equation: an element of a domain generated with the constructor Dom::LinearDifferentialFunction.
init - the initial conditions: a list of equations.
pars - the parameters: a list of identifiers.

Returns

a list of expressions representing the parametric solution of the differential equation for the given initial conditions.

Related Functions

detools::characteristics, detools::charODESystem, detools::pdesolve, solve

Details

Example 1

With the following input one can solve the linear differential equation 2 diff(u,x)+diff(u,y)+3 diff(u,z)-2 u=0 for the following parametrized initial condition x=2*sigma,y=3*tau,z=sigma+tau,u=sigma-tau.

>> LDF := Dom::LinearDifferentialFunction(
                Vars = [[x, y, z], u], Rest = [Types = "Indep"]):
   ldf := LDF( 2*u([x]) + u([y]) + 3*u([z]) - 2*u ):
   detools::charSolve(ldf, 
       {x = 2*sigma, y = 3*tau, z = sigma + tau, u = sigma - tau},
       {sigma, tau})
                   / 7 x   y   2 z \    / 6 z   2 y   3 x \
               u = | --- - - - --- | exp| --- - --- - --- |
                   \ 10    5    5  /    \  5     5     5  /




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