variation

variation - Compute the variation

Calling sequence:

variation(expr,var,dvar)

Parameters

expr - An expression containing the variables in var.

var - A variable, or a list of variables, to perform the variation with respect to.

dvar - the names of the variations of the variables in var. Must have same length as var

Synopsis:

Performs the variation of expression by replacing var by var + eps*dvar, differentiating with repect to eps, and substituting eps=0.
ElementInt and BoundaryInt commute with this differentiation, so that variations of integral forms expressed in ElementInt and BoundaryInt can be computed.
if var is a list, the chain rule is applied so that variation(expr,[u(x),v(x)],[du(x),dv(x)]) is equivalent to
variation(expr,u(x),du(x)) + variation(expr,v(x),dv(x))
expr can be a list, equality or a plain expression.

Examples:

> J:=ElementInt(u(x)^2); 2 J := ElementInt(u(x) ) > variation( J , u(x),du(x)); ElementInt(2 u(x) du(x)) > F:=ElementInt(u(x,y)^2 + v(x,y)^2); 2 2 F := ElementInt(u(x, y) + v(x, y) ) > variation(F,[u(x,y),v(x,y)],[du(x,y),dv(x,y)]); ElementInt(2 u(x, y) du(x, y)) + ElementInt(2 v(x, y) dv(x, y)) > BClist:=[u(x)=0,diff(u(x),x)=q]; d BClist := [u(x) = 0, -- u(x) = q] dx > variation(BClist,u(x),du(x)); d [du(x) = 0, -- du(x) = 0] dx