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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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.