An Introductory Guide to Computational Methods for the Solution of Physics Problems: With Emphasis on Spectral Methods (Lecture Notes in Physics) - Softcover

Buch 176�von 241: Lecture Notes in Physics

Rawitscher, George ; Dos Santos Filho, Victo ; Peixoto, Thiago Carvalho

9783319427027: An Introductory Guide to Computational Methods for the Solution of Physics Problems: With Emphasis on Spectral Methods (Lecture Notes in Physics)

Softcover

ISBN 10: 3319427024 ISBN 13: 9783319427027

Verlag: Springer, 2018

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This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally

taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to

the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of

appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via

collocation equations. The main advantage of these methods is that they simultaneously take into account all available

information, rather only the information available at a limited number of mesh points. They require more complicated

matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the

spectral methods more than compensates for anysuch drawbacks.

During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and

the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points

used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution

of integral equations.

The monograph includes an informative introduction to old and new computational methods with numerous practical examples,

while at the same time pointing out the errors that each of the available algorithms introduces into the specific

solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students

wishing to compare the available computational methods. In addition, the work develops the criteria required for

students to select the most suitable method to solve the particular scientific problem that they are confronting.

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�ber die Autorin bzw. den Autor

Born in Germany in 1928, George Rawitscher moved with his family to Sao Paulo, Brazil in 1934 in order to escape Nazi persecution. He studied Physics and Mathematics at the University of S. Paulo from 1945 to 1949, (with BA degrees), received his Ph.D. in Nuclear and Particle Physics in 1956 from Stanford University. After teaching at the University of Rochester and at Yale University, he went to the University of Connecticut in 1966 and rose to the rank of Full Professor in 1972. In 2009 he retired, and is now a Research Professor in UConn's physics department. His research specializations are in low energy nuclear physics and in computational methods. In addition to his continuing scientific physics involvements, his other interests are on World Order (UN transformation) and Climate Change.

Victo dos Santos Filho, born in 1967 in Lorena, S�o Paulo State, Brazil, studied Mathematics at the Universidade Salesiana de Lorena from 1985 to 1988, and in sequence he studied Physics at Universidade Estadual Paulista (UNESP) de Guaratinguet� from 1989 to 1992. He received his Master degree in Superconducting Technology in Funda��o de Tecnologia Industrial (FTI) in 1994 and his Ph.D. in 2001 in Theoretical Physics at Instituto de F�sica Te�rica (IFT) of UNESP, in the area of Bose-Einstein Condensates. After four years of post-doc in IFT concerning theoretical studies in Bose-Einstein Condensates with dissipative effects, he began to teach in private institutions of S�o Paulo. From 2015, he has worked in the H4D Scientific Laboratory Research as a scientific researcher in physics and technology. Among his recent scientific research interests are condensed matter physics, mathematical physics, general physics and computational physics.

Thiago Carvalho Peixoto graduated with a Bachelor degree in Physics in 2012 from the Federal University of Sergipe (UFS). He obtained a Master's Degree in Theoretical Physics in 2014 at the Theoretical Physics Institute of S�o Paulo's State University (UNESP). He worked as a professor of Physics at the Federal Institute of North of Minas Gerais (IFNMG) from 2016 to 2017 and nowadays he is professor of Physics at the Federal Institute of Sergipe (IFS).

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