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Two approximations of solutions of Hamilton-Jacobi equations. (English) Zbl 0556.65076

The paper is concerned with the approximation of solutions of the Cauchy problem for first order partial differential equations of Hamilton-Jacobi type. Two sorts of approximations are considered - finite difference schemes and the method of vanishing viscosity. The paper establishes the convergence of these difference approximations to suitable generalized solutions by obtaining explicit error estimates.
Reviewer: A.Varga

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
70H20 Hamilton-Jacobi equations in mechanics
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