Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

Numerical solutions of differential equations --- Differential equations --- Equations différentielles --- Numerical solutions --- Data processing --- Solutions numériques --- Informatique --- MATLAB --- Differential equations. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- MATLAB. --- Data processing. --- Equations différentielles --- Solutions numériques --- MATLAB (Computer program) --- Matrix laboratory --- MATLAB (Computer file) --- 517.91 Differential equations --- Differential equations - Numerical solutions - Data processing

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Differential equations --- Equations différentielles --- Numerical solutions. --- Solutions numériques --- 519.6 --- 681.3*G17 --- Computational mathematics. Numerical analysis. Computer programming --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.91 Differential equations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.

Differential equations --- Singular perturbations (Mathematics) --- Numerical solutions. --- Perturbation (Mathematics) --- 517.91 Differential equations --- Asymptotic theory --- Springer eBooks. --- Boundary value problems. --- Finite element method. --- Navier-Stokes equations. --- Numerical analysis. --- Singular perturbations (Mathematics). --- Équations différentielles --- Perturbations singulières (Mathématiques). --- Solutions numériques. --- Engineering mathematics. --- Global analysis (Mathematics). --- Statistics. --- Chemistry. --- Numerical Analysis. --- Mathematical and Computational Engineering. --- Analysis. --- Mathematical and Computational Biology. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Theoretical and Computational Chemistry. --- Physical sciences --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Engineering --- Engineering analysis --- Mathematical analysis --- Applied mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Biomathematics. --- Statistics . --- Chemistry, Physical and theoretical. --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Biology --- 517.1 Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents numerical differential quadrature (DQ) - based methods recently developed by the author. Their ability for solving generic scientific and engineering problems is demonstrated. These methods are the generic differential quadrature, the extended differential quadrature and the related discrete element analysis methods. These novel numerical techniques are both efficient and reliable. They are suitable for developing solution algorithms for various computational mechanics problems with arbitrarily complex geometry. This is shown for several comprehensive examples such as bars and beams, trusses, frames, general field problems, elasticity problems or bending of plates.

Differential equations --- Differential equations, Partial --- Equations différentielles --- Equations aux dérivées partielles --- Numerical solutions --- Solutions numériques --- Differential equations. --- Discrete element method --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Civil Engineering --- Calculus --- Numerical solutions. --- 517.91 Differential equations --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Physics. --- Computational intelligence. --- Mechanics. --- Mechanics, Applied. --- Analysis. --- Theoretical and Applied Mechanics. --- Computational Intelligence. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Numerical and Computational Physics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Intelligence, Computational --- Artificial intelligence --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Soft computing --- Numerical analysis --- Global analysis (Mathematics). --- Mechanics, applied. --- Engineering. --- Mathematical physics. --- Numerical and Computational Physics, Simulation. --- Physical mathematics --- Construction --- Industrial arts --- Technology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability densities. The book discusses in detail the construction of prior models, the measurement noise modeling and Bayesian estimation. Markov Chain Monte Carlo-methods as well as optimization methods are employed to explore the probability distributions. The results and techniques are clarified with classroom examples that are often non-trivial but easy to follow. Besides the simple examples, the book contains previously unpublished research material, where the statistical approach is developed further to treat such problems as discretization errors, and statistical model reduction. Furthermore, the techniques are then applied to a number of real world applications such as limited angle tomography, image deblurring, electrical impedance tomography and biomagnetic inverse problems. The book is intended to researchers and advanced students in applied mathematics, computational physics and engineering. The first part of the book can be used as a text book on advanced inverse problems courses. The authors Jari Kaipio and Erkki Somersalo are Professors in the Applied Physics Department of the University of Kuopio, Finland and the Mathematics Department at the Helsinki University of Technology, Finland, respectively.

Inverse problems (Differential equations) --- Problèmes inversés (Equations différentielles) --- Numerical solutions. --- Solutions numériques --- Inverse problems (Differential equations) -- Numerical solutions. --- Mathematics - General --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Numerical solutions --- Inverse problems (Differential equations). --- Problèmes inversés (Equations différentielles) --- Solutions numériques --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Probabilities. --- Physics. --- Complexity, Computational. --- Biomedical engineering. --- Probability Theory and Stochastic Processes. --- Analysis. --- Computational Mathematics and Numerical Analysis. --- Theoretical, Mathematical and Computational Physics. --- Complexity. --- Biomedical Engineering. --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Medicine --- Complexity, Computational --- Electronic data processing --- Machine theory --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Computer mathematics --- Discrete mathematics --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Numerical analysis --- Differential equations --- Distribution (Probability theory. --- Global analysis (Mathematics). --- Computer science --- Engineering. --- Biomedical Engineering and Bioengineering. --- Construction --- Industrial arts --- Technology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical physics. --- Computational complexity. --- Physical mathematics --- Physics --- Inverse problems (Differential equations) - Numerical solutions.