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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Paperback. Condizione: New. Print on Demand. This book delves into the realm of solving complex mathematical equations that model real-world phenomena with high accuracy. The author delves into the intricacies of difference schemes, numerical approximations used to solve these equations, focusing on second-order accuracy to minimize errors. The book meticulously analyzes the stability of these schemes, a crucial factor in ensuring reliable solutions over time. Additionally, it explores the application of these schemes to systems of conservation laws, equations that describe the behavior of fluids and gases. Through rigorous analysis and practical examples, this book equips mathematicians, physicists, and engineers with a comprehensive understanding of difference schemes, enabling them to tackle complex simulations with confidence. Its insights advance the field of numerical analysis and contribute to the wider pursuit of scientific knowledge. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781330147429_0
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