ABSTRACT
An optimum computer methodology for nonlinear DE systems, direct, formal integration (DFI), requires only one numeric approximation and has had wide success in nonlinear physics. A partial list of applications include: superson-ics, nonlinear heat conduction, Laplace, 3-D Navier-Stokes, and 4-D turbulent channel flows. Major DFI modes are “SIMPLEX”, one integration trajectory, and “NAD”, a distinct trajectory for each variable. DE systems yield readily to DFI; integral methods are more compatible to digital machines. DFI has many major appeals Natural anti-derivative eliminates all derivatives; optimum machine compatibility; iterations are often unneeded; uniqueness assured for technology; multiple algorithms; analytics near IP provide new insights; “micro”-Picard saves CPU time; easy global and local checks; tiny FORTRAN codes: the elliptic solver has 16 lines and hyperbolic solver has 13 lines.
