Analytical Solution Methods For Boundary Value Problems

Name: Analytical Solution Methods For Boundary Value Problems
Brand: Elsevier
SKU: 9780128042892
Price: 5971.0 INR
Availability: InStock

by A.S. Yakimov

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ISBN13: 9780128042892
Binding: Hardcover
Subject: Mathematics and Statistics
Publisher: Elsevier
Publisher Imprint: Acad Pr
Publication Date: September 16, 2017
Pages: 232
Original Price: USD 99.95
Language: English
Edition: N/A
Item Weight: 450 grams
BISAC Subject(s): Differential Equations / Ordinary

About The Book

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods.

About The Author

Yakimov, A. S.: - AS. Yakimov (the Department of Physical and Computational Mechanics, Tomsk State University, Tomsk, Russia). Anatoly Stepanovich Yakimov is a Senior Fellow and Professor of the Department of Physical and Computational Mechanics of Tomsk State University, Russia. He is the author of text-books, monographs and 70 scientific publications devoted to the mathematical modeling of the thermal protection and the development of mathematical technology solution of mathematical physics equations.

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