Difference Schemes With High Order of Accuracy for Solving Hyperbolic Equations (Classic Reprint)

Excerpt from Difference Schemes With High Order of Accuracy for Solving Hyperbolic Equations

It is well Known that a difference scheme, in order to furnish accurate answers over a reasonably long range of time has to be stable. The bulk of this paper is devoted to determining the conditions under which the proposed dif ference schemes are stable.

In Section 1 we give a brief review of the general theory of accuracy and stability of difference schemes. In Section 2 we show that the set of matrices whose field of value belongs to the unit circle forms a stable family.

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