**Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations**

English | 2024 | ISBN: 1108490999 | 741 Pages | PDF | 17 MB

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English | 2024 | ISBN: 1108490999 | 741 Pages | PDF | 17 MB

English | ISBN: 906764336X | 2001 | 112 pages | PDF | 3 MB

English | August 23, 2024 | ISBN: N/A | ASIN: B0DF61M5J1 | 56 pages | EPUB | 4.11 Mb

English | PDF | 1999 | 308 Pages | ISBN : 3540761241 | 15.3 MB

The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.

English | ISBN: 1611976421 | 2021 | 289 pages | PDF | 39 MB

English | ISBN: 0534373887 | 2000 | 520 pages | RAR | 269 MB

English | ISBN: 3110151138 | 2011 | 557 pages | PDF | 17 MB

English | 2024 | ISBN: 1032662522 | 452 Pages | PDF (True) | 22 MB

English | November 3, 2023 | ISBN: N/A | ASIN: B0CMNDRYFQ | 377 pages | PDF | 76 Mb

English | 2024 | ISBN: 303154241X | 411 Pages | PDF EPUB (True) | 39 MB

Methusalem Workshop on Classical Analysis and Partial Differential Equations

English | 2024 | ISBN: 3031416643 | 249 Pages | PDF EPUB (True) | 20 MB

English | 2017 | pages: 200 | ISBN: 8120352807 | PDF | 4,0 mb

English | 2024 | ISBN: 1009278908 | 445 Pages | PDF | 15 MB

English | ISBN: 1470472457 | 2023 | 505 pages | PDF | 8 MB

English | PDF | 1972 | 495 Pages | ISBN : 940102717X | 32 MB

One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.