Global Series Solutions of Nonlinear Differential Equations with Shocks using Walsh Functions

An orthonormal basis set is introduced for use in generating global solutions to nonlinear differential equations with shocks. By global, it is meant that a single series solution is generated that is valid over the entire domain, not a separate solution across discretized elements of the domain. Its derivation was motivated by shortcomings in all current computational fluid dynamic algorithms for dealing with complex, hypersonic flows involving interacting shocks. The fractal-like derivation (infinitely self-similar) focused on the distribution of segment lengths yields a scaled set of Walsh functions.