Numerical Solution of Partial Differential Equations: An Introduction by K. W. Morton |
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‘This book can be highly recommended as a basis for courses in numerical analysis.’ Zentralblatt fur Mathematik
‘I believe this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations.’ J. Varah, Computing Reviews
‘… nicely crafted and full of interesting details.’ R. Mattheij, ITW Nieuws
‘… a well written and exciting book … the exposition throughout the book is clear and very lively. The author’s enthusiasm and wit are obvious on almost every page and I recommend the text very strongly indeed.’ J. Mackenzie, Proceedings of the Edinburgh Mathematical Society
‘This is a well-written, challenging introductory text that addresses the essential issues in the development of effective numerical schemes for the solution of differential equations: stability, convergence, and efficiency. The soft cover edition is a terrific buy - I highly recommend it.‘ Tom King, Mathematics of Computation
‘I believe this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations.’ J. Varah, Computing Reviews
‘… nicely crafted and full of interesting details.’ R. Mattheij, ITW Nieuws
‘… a well written and exciting book … the exposition throughout the book is clear and very lively. The author’s enthusiasm and wit are obvious on almost every page and I recommend the text very strongly indeed.’ J. Mackenzie, Proceedings of the Edinburgh Mathematical Society
‘This is a well-written, challenging introductory text that addresses the essential issues in the development of effective numerical schemes for the solution of differential equations: stability, convergence, and efficiency. The soft cover edition is a terrific buy - I highly recommend it.‘ Tom King, Mathematics of Computation
Product Description
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance between theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. Dr Iserles concentrates on fundamentals: deriving methods from first principles, analysing them with a variety of mathematical techniques and occasionally discussing questions of implementation and applications. By doing so, he is able to lead the reader to theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations.
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