Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations of variations, control theory and differential games. Recently Crandall and Lions established the correct notion of generalized solutions for these equations. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations. These include max-min representations of solutions relevant to the theory of differential games which imply the existence of the value of the game, representations as limits of solutions of general explicit and implicit finite difference schemes, and as limits of several types of Trotter products. Author
- Numerical Mathematics