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D.15.8.11 midpoint

Procedure from library finitediff.lib (see finitediff_lib).

Usage:
midpoint(U1,U2,var); U1, U2 are the names of occuring derivatives, var is a variable in the basering;

Return:
type vector; gives a predefined approximation of the midpoint-approximation as often used in literature;

Note:
see also forward,laxfrT,setinitials,scheme;

Example:
 
LIB "finitediff.lib";
list D="Uxx","Ux","Utt","Ut","U";
list P="lambda";
list V="t","x";
setinitials(V,D,P);
midpoint(Ux,U,x);
==> [0,(2*dx)*x,0,0,-x^2+1]