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Excerpt from Differential Equations, Difference Equations and Matrix Theory
In section A we apply one of the matrix theorems of section 3 to derive a criterion for the stability of difference schemes used to approximate solutions of differential equations. This criterion is an extension from the symmetric to the nonsymmetric case of Friedrichs' stability theorem for difference equations with positive coefficients. Applications to various specific difference schemes are given at the end of the section.
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Differential Equations, Difference Equations and Matrix Theory
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Paperback. Condizione: New. Print on Demand. This thought-provoking book explores the interplay between hyperbolic systems of differential and difference equations, examining the theoretical underpinnings of their stability and convergence. The author, a highly regarded mathematician, presents a novel approach to proving stability that extends the celebrated Friedrichs' criterion to non-symmetric systems. The book demonstrates how this extended criterion can be applied to various difference schemes, offering a deeper understanding of their behavior. Furthermore, the author delves into the mathematical properties of the eigenvalues of matrices associated with these systems, revealing their convexity and monotonicity. This work contributes significantly to the understanding of numerical methods for solving hyperbolic equations and provides valuable insights for researchers and practitioners in applied mathematics and computational science. 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 9781330134054_0
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