Deferred approach to the limit in non-linear hyperbolic systems

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Abstract
In the numerical solution of systems of hyperbolic partial differential equations by finite difference methods, it is often the case that the data given to make the differential problem well posed under-determines the difference problem. The problem of determining the data to make the difference problem well posed is considered and techniques for introducing the extra required data are introduced. In the solution of ordinary differential equations. Richardson's deferred approach to the limit has long been well known. Only recently has this extrapolation scheme been applied to some categories of partial differential equations. In this paper we will show how the boundary techniques mentioned above may be utilised in an important way in order that the extrapolation procedure may be used. Several numerical examples are quoted.

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