Singular Manual: midpoint

| #### D.15.4.11 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]

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