Many complex problems of social life put forward new demands for science and technology. It is quite obvious that further progress is impossible without methodological renovation of science. Mathematical modelling and computational experiment make the basis for such renewal. It lies in spreading the expertise, ideas and methods of applied mathematics to new spheres. The main purpose of this proceedings is to bring together the scientists in applied mathematics and computational experiment, developers and users of mathematical models from different branches of knowledge in order to exchange ideas, information and experience. The volume contributes to a deeper understanding of contemporary interdisciplinary problems.

Mathematical Modelling and Applied Mathematics: Proceedings of the Imacs International Conference on Mathematical Modelling and Applied Mathematics

Science & Math

Samarskii, A.A.

Mathematics

North-Holland

This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches to the analysis of the models by traditional means of applied mathematics are described. Numerical methods for the approximate solution of steady and unsteady-state heat conduction problems are discussed. Investigation of difference schemes is based on the general stability theory. Much emphasis is put on problems in which phase transitions are involved and on heat and mass transfer problems. Problems of controlling and optimizing heat processes are discussed in detail. These processes are described by partial differential equations, and the main approaches to numerical solution of the optimal control problems involved here are discussed. Aspects of numerical solution of inverse heat exchange problems are considered. Much attention is paid to the most important applied problems of identifying coefficients and boundary conditions for a heat transfer equation. This first volume considers the mathematical models of heat transfer, classic analytical solution methods for heat conduction problems, numerical methods for steady-state and transient heat conduction problems, and phase change problems. The second volume presents solution techniques for complicated heat transfer problems (radiation, convection, thermoelasticity, thermal process control and inverse problems) as well as some examples of solving particular heat transfer problems.

Mathematical Modelling, Volume 1, Computational Heat Transfer

Vabishchevich, P.N.

Physics

wiley

This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches, to the analysis of the models by traditional means of applied mathematics are described. Numerical methods for the approximate solution of steady- and unsteady state heat conduction problems are discussed. Investigation of difference schemes is based on the general stability theory. Much emphasis is put on problems in which phase transitions are involved and on heat and mass transfer problems. Problems of controlling and optimizing heat processes are discussed in detail. These processes are described by partial differential equations, and the main approaches to numerical solution of the optimal control problems involved here are discussed. Aspects of numerical solution of inverse heat exchange problems are considered. Much attention is paid to the most important applied problems of identifying coefficients and boundary conditions for a heat transfer equation. The first volume considered the mathematical models of heat transfer, classic analytical solution methods for heat conduction problems, numerical methods for steady-state and transient heat conduction problems, and phase change problems. In this second volume, we present solution techniques for complicated heat transfer problems (radiation, convection, thermoelasticity, thermal process control and inverse problems) as well as some examples of solving particular heat transfer problems.

The Finite Difference Methodology, Volume 2, Computational Heat Transfer

Research

Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.

Equations of Mathematical Physics (Dover Books on Physics)

Tikhonov, A.N.

Dover Publications

This is the sixth edition of a text that has been in use since the 1950s; it has been substantially revised and reflects developments in mathematical physics at the end of the 20th century.

Equations of Mathematical Physics (Russian Research in Mathematics and Science)

Reference

Foreign Language Study & Reference

The Edwin Mellen Press Ltd

Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta bility of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various di rections. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tad more [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solu tion to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori es timates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence.

Difference Schemes with Operator Factors (Mathematics and Its Applications, 546)

Matus, P.P.

Springer

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Blow-Up in Quasilinear Parabolic Equations (De Gruyter Expositions in Mathematics, 19)

Galaktionov, Victor A.

Kurdyumov, Sergey p.

Mikhailov, A. P.

de Gruyter

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

Numerical Methods for Solving Inverse Problems of Mathematical Physics (Inverse and Ill-Posed Problems Series, 52)

Vabishchevich, Petr N.

Evolution

See the best price to sell, buy, or rent books by Samarskii, A.A.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Samarskii, A.A.

See the best price to sell, buy, or rent books by Samarskii, A.A.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Mathematical Modelling and Applied Mathematics: Proceedings of the Imacs International Conference on Mathematical Modelling and Applied Mathematics

Mathematical Modelling, Volume 1, Computational Heat Transfer

The Finite Difference Methodology, Volume 2, Computational Heat Transfer

Equations of Mathematical Physics (Dover Books on Physics)

Equations of Mathematical Physics (Russian Research in Mathematics and Science)

Equations of Mathematical Physics (Russian Research in Mathematics and Science)

Difference Schemes with Operator Factors (Mathematics and Its Applications, 546)

Blow-Up in Quasilinear Parabolic Equations (De Gruyter Expositions in Mathematics, 19)

Numerical Methods for Solving Inverse Problems of Mathematical Physics (Inverse and Ill-Posed Problems Series, 52)