ABSTRACT
The method, “DFI” (Direct, Formal Integration), has advantage over FDM and other DE solvers as cited in Payne [1-3]. DFI eliminates all derivatives in its full implementation, “NAD” (Natural Anti-Derivative). Five non-linear DE systems are treated: three ODEs display various basic facets of DFI; two PDEs further the methodology. ODEs are Riccati, a boundary-layer model and Blasius flow. PDEs are Euler and inviscid Burger which, as two ODES, has an exact solution, ideal for numerical development. DFI reproduces exact solutions limited only by machine precision. This happy circumstance is attributed to the smoothing action of integration and its implementation, evading any finite differencing. Granted, none of the problems are of “real-world” technological interest, but all impact how such problems are solved. “DFI” is defined and applied to Riccati (first order) and a “model” (second order); each has exact solution to check precisely the numerics. A third order ODE, Blasius, shows a plethora of alternate, useful algorithms which DFI provides any DE higher order than one. Unpublished work on 2-D, steady, incompressible Euler is summarized and inviscid Burger is deeply explored (grid sizes, predictors,...).
