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Stochastic solutions provide new rigorous results for nonlinear PDE’s and, through its local nongrid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions: McKean’s and superprocesses. In favour of superprocesses is the fact that they handle arbitrary boundary conditions. However, when restricted to measures, superprocesses can only be used to generate solutions for a limited class of nonlinear PDE’s. A new class of superprocesses, namely superprocesses on ultradistributions, is proposed to extend the stochastic solution approach to a wider class of PDE’s. [ABSTRACT FROM AUTHOR]

The stochastic construction of solutions for nonlinear partial differential equations is discussed. The technique provides new exact solutions and efficient numerical codes for localized solutions and parallel computing. A brief review of known solutions and some new results for the Poisson-Vlasov and Euler equations are included. [ABSTRACT FROM AUTHOR]