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Evolution equations --- Numerical solutions --- Differential equations [Parabolic] --- Evolution equations - Numerical solutions. --- Differential equations, Parabolic - Numerical solutions. --- Differential equations, Parabolic --- Evolution equations - Numerical solutions --- Differential equations, Parabolic - Numerical solutions
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This book collects, explains and analyses basic methods and recent results for the successful numerical solution of singularly perturbed differential equations. Such equations model many physical phenomena and their solutions are characterized by the presence of layers. The book is a wide-ranging introduction to the exciting current literature in this area. It concentrates on linear convection-diffusion equations and related nonlinear flow problems, encompassing both ordinary and partial differential equations. While many numerical methods are considered, particular attention is paid to those with realistic error estimates. The book provides a solid and thorough foundation for the numerical analysis and solution of singular perturbation problems.
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Symmetry is the key to solving differential equations. There are many well-known techniques for obtaining exact solutions, but most of them are special cases of a few powerful symmetry methods. Furthermore, these methods can be applied to differential equations of an unfamiliar type; they do not rely on special 'tricks'. Instead, a given differential equation is forced to reveal its symmetries, which are then used to construct exact solutions. This book is a straightforward introduction to the subject, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily. The book contains methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.
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Berekeningen [Ingewikkeldheid van ] --- Calcul [Complexité de ] --- Complexité de calcul --- Computational complexity --- Ingewikkeldheid van berekeningen --- Differential equations --- Integral equations --- Computational complexity. --- Numerical solutions. --- Numerical solutions --- Differential equations - Numerical solutions. --- Integral equations - Numerical solutions.
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Numerical solutions of algebraic equations --- Equations --- Polynomials --- numerical solutions --- congresses --- Congresses --- Equations - numerical solutions - congresses --- Polynomials - Congresses
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