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Excerpt from On the Partial Difference Equations, of Mathematical Physics
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Excerpt from On the Partial Difference Equations, of Mathematical Physics
Nyo-7689 of arbitrarily high order tends to the corresponding deriva tive. Nowhere do we assume the existence of the solution to the differential equation problem on the contrary, we obtain a simple existence proof by using the limiting processi. For the case of elliptic equations convergence is obtained independently of the choice of mesh, but we will find that for the case of the initial value problem for hyperbolic equations, convergence is obtained only if the ratio of the mesh widths in different directions satis fies certain inequalities which ih turn depend on the position of the characteristics relative to the mesh.
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.
Reseña del editor
Excerpt from On the Partial Difference Equations, of Mathematical Physics
This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report.
As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor.
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.
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On the Partial Difference Equations, of Mathematical Physics (Classic Reprint)
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On the Partial Difference Equations, of Mathematical Physics (Classic Reprint)
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On the Partial Difference Equations, of Mathematical Physics (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book delves into the fascinating world of partial difference equations, a powerful mathematical tool used to solve complex problems in physics and other scientific fields. The author explores how these equations can be used to approximate solutions to classic linear partial differential equations, which are notoriously difficult to solve directly. The book focuses on three key areas: elliptic, hyperbolic, and parabolic cases of partial difference equations. It investigates how solutions to these equations behave when the mesh width, a crucial element in the discretization of continuous variables, approaches zero. This process, known as "convergence," is crucial for ensuring that the solutions of the difference equations accurately reflect the behavior of the corresponding differential equations. The author's analysis reveals that the convergence of solutions depends critically on the relationship between the mesh width and the characteristics of the differential equations. This book offers a groundbreaking approach to the study of partial difference equations, paving the way for a deeper understanding of their applications in a wide range of scientific disciplines. 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. Bestandsnummer des Verkäufers 9781330102756_0
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On the Partial Difference Equations, of Mathematical Physics (Classic Reprint)
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Paperback. Zustand: Brand New. 96 pages. 5.60x3.80x0.01 inches. This item is printed on demand. Bestandsnummer des Verkäufers zk1330102754
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