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Introduction to Computation and Modeling for Differential Equations

Author: Lennart Edsberg

Publisher: John Wiley & Sons

Published: 2015-10-05

Total Pages: 285

ISBN-13: 1119018447

Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.

Computational Differential Equations

Author: Kenneth Eriksson

Publisher: Cambridge University Press

Published: 1996-09-05

Total Pages: 558

ISBN-13: 9780521567381

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This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

Partial Differential Equations

Author: R. M. M. Mattheij

Publisher: SIAM

Published: 2005-01-01

Total Pages: 689

ISBN-13: 0898715946

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Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.

Introduction to Computation and Modeling for Differential Equations

Author: Lennart Edsberg

Publisher: John Wiley & Sons

Published: 2015-09-16

Total Pages: 288

ISBN-13: 1119018463

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An Invitation to Applied Mathematics

Author: Carmen Chicone

Publisher: Academic Press

Published: 2016-09-24

Total Pages: 878

ISBN-13: 0128041544

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An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested

Partial Differential Equations

Author: R. M. M. Mattheij

Publisher: SIAM

Published: 2005-01-01

Total Pages: 697

ISBN-13: 9780898718270

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Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.

Introduction to Elementary Computational Modeling

Author: Jose Garrido

Publisher: CRC Press

Published: 2011-10-26

Total Pages: 331

ISBN-13: 1439867399

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With an emphasis on problem solving, this book introduces the basic principles and fundamental concepts of computational modeling. It emphasizes reasoning and conceptualizing problems, the elementary mathematical modeling, and the implementation using computing concepts and principles. Examples are included that demonstrate the computation and visualization of the implemented models. The author provides case studies, along with an overview of computational models and their development. The first part of the text presents the basic concepts of models and techniques for designing and implementing problem solutions. It applies standard pseudo-code constructs and flowcharts for designing models. The second part covers model implementation with basic programming constructs using MATLAB®, Octave, and FreeMat. Aimed at beginning students in computer science, mathematics, statistics, and engineering, Introduction to Elementary Computational Modeling: Essential Concepts, Principles, and Problem Solving focuses on fundamentals, helping the next generation of scientists and engineers hone their problem solving skills.

Differential Equations, Mechanics, and Computation

Author: Richard S. Palais

Publisher: American Mathematical Soc.

Published: 2009-11-13

Total Pages: 329

ISBN-13: 0821821385

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This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.

Computational Differential Equations

Author: K. Eriksson

Publisher: Cambridge University Press

Published: 1996-09-05

Total Pages: 554

ISBN-13: 9780521563123

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This is a two volume introduction to the computational solution of differential equations using a unified approach organized around the adaptive finite element method. It presents a synthesis of mathematical modeling, analysis, and computation. The goal is to provide the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modeling in science and engineering: How can we model physical phenomena using differential equations? What are the properties of solutions of differential equations? How do we compute solutions in practice? How do we estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The authors then widen the scope to cover the basic classes of linear partial differential equations modeling elasticity, heat flow, wave propagation and convection-diffusion-absorption problems. The book concludes with a chapter on the abstract framework of the finite element method for differential equations. Volume 2, to be published in early 1997, extends the scope to nonlinear differential equations and systems of equations modeling a variety of phenomena such as reaction-diffusion, fluid flow, many-body dynamics and reaches the frontiers of research. It also addresses practical implementation issues in detail. These volumes are ideal for undergraduates studying numerical analysis or differential equations. This is a new edition of a 1988 text of 275 pages by C. Johnson.

An Introduction to Computational Science

Author: Allen Holder

Publisher: Springer

Published: 2019-06-18

Total Pages: 470

ISBN-13: 3030156796

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This textbook provides an introduction to the growing interdisciplinary field of computational science. It combines a foundational development of numerical methods with a variety of illustrative applications spread across numerous areas of science and engineering. The intended audience is the undergraduate who has completed introductory coursework in mathematics and computer science. Students gain computational acuity by authoring their own numerical routines and by practicing with numerical methods as they solve computational models. This education encourages students to learn the importance of answering: How expensive is a calculation, how trustworthy is a calculation, and how might we model a problem to apply a desired numerical method? The text is written in two parts. Part I provides a succinct, one-term inauguration into the primary routines on which a further study of computational science rests. The material is organized so that the transition to computational science from coursework in calculus, differential equations, and linear algebra is natural. Beyond the mathematical and computational content of Part I, students gain proficiency with elemental programming constructs and visualization, which are presented in MATLAB syntax. The focus of Part II is modeling, wherein students build computational models, compute solutions, and report their findings. The models purposely intersect numerous areas of science and engineering to demonstrate the pervasive role played by computational science.