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detools::transform -- change of variables for differential equations

Introduction

detools::transform performs variable transformations in differential equations.

Call(s)

detools::transform(de, indl, depl, mode, <, NewVars = varl> <ChangeOfVars = cl>)

Parameters

de - the differential equation: an expression.
indl - the independent variable(s): a list of (indexed) identifiers.
depl - the dependent variable(s): a list of (indexed) identifiers.
mode - transformation mode: either the string Ïndep" or "Dep".

Options

NewVars - lists the names of the new variables.
ChangeOfVars - defines the new variables.

Returns

an expression.

Details

Example 1

We transform the independent variables in a simple linear differential expression. Note that the new variables are given as linear functions of the old ones.

>> detools::transform(u([x]) + u([y]), [x, y], [u], NewVars = [X, Y], 
                 ChangeOfVars = [X = x + y, Y = x - y], "Indep")
                                 2 u([X])

Example 2

Now we transform the dependent variable. Here the old variable must be given as a linear function of the new one.

>> detools::transform(u([x]) + u([y]), [x, y], [u], NewVars = [U], 
                 ChangeOfVars = [u=3*U], "Dep")
                            3 U([x]) + 3 U([y])




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