New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics
New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics

Author: Mustafa Inc

Publisher: Frontiers Media SA

Published: 2023-11-20

Total Pages: 160

ISBN-13: 2832539432

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Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws

New Tools for Nonlinear PDEs and Application
New Tools for Nonlinear PDEs and Application

Author: Marcello D'Abbicco

Publisher: Springer

Published: 2019-05-07

Total Pages: 392

ISBN-13: 3030109372

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This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.

Nonlinear Partial Differential Equations for Scientists and Engineers
Nonlinear Partial Differential Equations for Scientists and Engineers

Author: Lokenath Debnath

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 602

ISBN-13: 1489928464

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This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.

Handbook of Linear Partial Differential Equations for Engineers and Scientists
Handbook of Linear Partial Differential Equations for Engineers and Scientists

Author: Andrei D. Polyanin

Publisher: CRC Press

Published: 2001-11-28

Total Pages: 800

ISBN-13: 1420035320

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Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with

Numerical and Analytical Methods in Electromagnetics
Numerical and Analytical Methods in Electromagnetics

Author: Hristos T. Anastassiu

Publisher: MDPI

Published: 2021-03-19

Total Pages: 196

ISBN-13: 3036500642

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Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics.

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations
Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations

Author: Santanu Saha Ray

Publisher: CRC Press

Published: 2018-01-12

Total Pages: 251

ISBN-13: 1351682210

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The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

Basic Partial Differential Equations
Basic Partial Differential Equations

Author: David. Bleecker

Publisher: CRC Press

Published: 2018-01-18

Total Pages: 765

ISBN-13: 1351078534

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Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.

Partial Differential Equations
Partial Differential Equations

Author: Walter A. Strauss

Publisher: John Wiley & Sons

Published: 2007-12-21

Total Pages: 467

ISBN-13: 0470054565

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Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Nonlinear Partial Differential Equations with Applications
Nonlinear Partial Differential Equations with Applications

Author: Tomás Roubicek

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 415

ISBN-13: 3764373970

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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.