Numerical Models for Differential Problems

Numerical Models for Differential Problems

Author: Alfio Quarteroni

Publisher: Springer Science & Business

Published: 2014-04-25

Total Pages: 668

ISBN-13: 8847055229

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In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.


Applied Numerical Modelling for Engineers

Applied Numerical Modelling for Engineers

Author: Donard De Cogan

Publisher: Oxford University Press, USA

Published: 1997

Total Pages: 296

ISBN-13:

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This is a broad ranging introductory text on applied numerical modelling and simulation. It covers many techniques and develops the relevant mathematics in parallel. The material is presented in the context of realistic practical examples. Many of the end-of-chapter exercises may be treated as open-ended projects which can be easily extended. The presentation makes the text easy to assimilate with a progression of concepts chapter by chpater. The more difficult material is assembled towards the end of the book. Each chapter has a list of references to accessible texts as well as journal publications which should provide pointers for research projects. The provision of software code in a range of languages should help the user to make rapid use of the material. This textbook will broaden the understanding of engineers and others using models leading to better and more productive modelling.


Geometric Modelling, Numerical Simulation, and Optimization:

Geometric Modelling, Numerical Simulation, and Optimization:

Author: Geir Hasle

Publisher: Springer Science & Business Media

Published: 2007-06-10

Total Pages: 559

ISBN-13: 3540687831

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This edited volume addresses the importance of mathematics for industry and society by presenting highlights from contract research at the Department of Applied Mathematics at SINTEF, the largest independent research organization in Scandinavia. Examples range from computer-aided geometric design, via general purpose computing on graphics cards, to reservoir simulation for enhanced oil recovery. Contributions are written in a tutorial style.


A Guide to Numerical Modelling in Systems Biology

A Guide to Numerical Modelling in Systems Biology

Author: Peter Deuflhard

Publisher: Springer

Published: 2015-07-06

Total Pages: 185

ISBN-13: 3319200593

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This book is intended for students of computational systems biology with only a limited background in mathematics. Typical books on systems biology merely mention algorithmic approaches, but without offering a deeper understanding. On the other hand, mathematical books are typically unreadable for computational biologists. The authors of the present book have worked hard to fill this gap. The result is not a book on systems biology, but on computational methods in systems biology. This book originated from courses taught by the authors at Freie Universität Berlin. The guiding idea of the courses was to convey those mathematical insights that are indispensable for systems biology, teaching the necessary mathematical prerequisites by means of many illustrative examples and without any theorems. The three chapters cover the mathematical modelling of biochemical and physiological processes, numerical simulation of the dynamics of biological networks and identification of model parameters by means of comparisons with real data. Throughout the text, the strengths and weaknesses of numerical algorithms with respect to various systems biological issues are discussed. Web addresses for downloading the corresponding software are also included.


Numerical Modeling of Coupled Phenomena in Science and Engineering

Numerical Modeling of Coupled Phenomena in Science and Engineering

Author: Mario César Suárez Arriaga

Publisher: CRC Press

Published: 2008-12-01

Total Pages: 496

ISBN-13: 0203886224

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Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book cont


Introduction to Numerical Geodynamic Modelling

Introduction to Numerical Geodynamic Modelling

Author: Taras Gerya

Publisher: Cambridge University Press

Published: 2010

Total Pages: 359

ISBN-13: 0521887542

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This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.


Numerical Modelling in Robotics

Numerical Modelling in Robotics

Author: Edgar Alonso Martínez García

Publisher: OmniaScience

Published: 2015-10-06

Total Pages: 467

ISBN-13: 8494211889

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Modern robotic systems are tied to operate autonomously in real-world environments performing a variety of complex tasks. Autonomous robots must rely on fundamental capabilities such as locomotion, trajectory tracking control, multi-sensor fusion, task/path planning, navigation, and real-time perception. Combining this knowledge is essential to design rolling, walking, aquatic, and hovering robots that sense and self-control. This book contains a mathematical modelling framework to support the learning of modern robotics and mechatronics, aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners. The volume exposes a solid understanding of mathematical methods as a common modelling framework to properly interpret advanced robotic systems. Including numerical approximations, solution of linear and non-linear systems of equations, curves fitting, differentiation and integration of functions. The book is suitable for courses on robotics, mechatronics, sensing models, vehicles design and control, modelling, simulation, and mechanisms analysis. It is organised with 17 chapters divided in five parts that conceptualise classical mechanics to model a wide variety of applied robotics. It comprehends a hover-craft, an amphibious hexapod, self-reconfiguration and under-actuation of rolling and passive walking robots with Hoekens, Klann, and Jansen limbs for bipedal, quadruped, and octapod robots.