Question: cannot find the error in loop

cannot find the error in loop

 

 

> restart; u[0] := (4/3)*c^2*cos((1/4)*x)^2; alpha := 2;
 
> iteration := 3;
> for k from 0 while k <= Iteration do u[s] := eval(u[k], t = xi); u[k+1] := simplify(u[k]-(int(diff(u[s], [`$`(xi, alpha)])+diff(u[s]*u[s], x)+diff(u[s]*u[s], x, x, x), xi = 0 .. t))) end do;

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