Multiresolution algorithms for the numerical solution of hyperbolic conservation laws. (English) Zbl 0860.65078

This paper presents a class of multiresolution algorithms for the numerical solution of an initial value problem for hyperbolic conservation laws in one space dimension. The paper considers a situation where the solution is highly nonuniform in its behaviour as a function of the space coordinates. The author presents a multiresolution alternative to the adaptive grid methodology in which one performs the uniform fine-grid computation to a prescribed accuracy but reduces the number of arithmetic operations and computer memory requirements to the level of an adaptive grid computation. The author also presents a sample of numerical experiments and makes observations about the accumulation of error.
Reviewer: V.P.Tyagi (Bombay)


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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