A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics, Series Number 15)

This book 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 among 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; and 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. cover......Page 1 A First Course in the Numerical Analysis of Differential Equations......Page 2 Contents......Page 4 Preface......Page 8 Flowchart of contents......Page 14 PART I Ordinary differential equations......Page 16 1 Euler's method and beyond......Page 18 2 Multistep methods......Page 34 3 Runge-Kutta methods......Page 48 4 Stiff equations......Page 68 5 Error control......Page 88 6 Nonlinear algebraic systems......Page 106 PART II The Poisson equation......Page 118 7 Finite digerence schemes......Page 120 8 The finite element method......Page 150 9 Gaussian elimination for sparse linear equations......Page 184 10 Iterative methods for sparse linear equations......Page 200 11 Multigrid techniques......Page 242 12 Fast Poisson solvers......Page 260 PART III Partial dinerential equations of evolution......Page 282 13 The digusion equation......Page 284 14 Hyperbolic equations......Page 322 Appendix Bluner's guide to useful mathematics......Page 362 A.1 Linear algebra......Page 363 A.2 Analysis......Page 374 Index......Page 382 Numerical analysis presents different faces to the world. It is the tension between standpoints that 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. Covers numerical analysis for mathematics students without neglecting practical aspects Arieh Iserles. Includes Bibliographical References And Index.