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519.6 --- 681.3 *G18

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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.

differentiaalvergelijking --- wiskunde --- numerieke analyse --- Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differential equations --- 519.62 --- 681.3 *G18 --- 519.62 Numerical methods for solution of ordinary differential equations --- Numerical methods for solution of ordinary differential equations --- 517.91 Differential equations --- Numerical solutions --- 517.91 --- Numerical solutions. --- Numerical analysis. --- Equations différentielles --- Solutions numériques --- Numerical solutions&delete& --- Differential equations - Numerical solutions. --- Acqui 2006 --- Analyse numerique --- Equations differentielles --- Equations aux derivees partielles

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Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differential equations, Partial --- 519.6 --- 681.3 *G18 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Numerical analysis --- Numerical solutions --- Numerical solutions. --- Equations aux dérivées partielles --- Solutions numériques --- Differential equations [Partial ] --- Finite differences --- Analyse numérique --- Différences finies --- Analyse numérique. --- Différences finies. --- Numerical analysis. --- Analyse numérique --- Différences finies --- Differential equations, Partial - Numerical solutions --- Equations aux derivees partielles --- Methodes numeriques --- Differences finies

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Eindige elementen [Methode van ] --- Elements finis [Methode des ] --- Finite element method --- Error analysis (Mathematics) --- Numerical analysis --- Erreurs, Théorie des --- Analyse numérique --- Differential equations, Elliptic --- -Differential equations, Nonlinear --- -Error analysis (Mathematics) --- 519.6 --- 681.3 *G18 --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Statistics --- Nonlinear differential equations --- Nonlinear theories --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differential equations, Nonlinear --- Numerical solutions. --- Error analysis (Mathematics). --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Erreurs, Théorie des --- Analyse numérique

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519.71 --- #TWER:MOD --- 681.3 *G18 --- 681.3*G17 --- Control systems theory: mathematical aspects --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 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) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.71 Control systems theory: mathematical aspects --- Automatic control --- Control theory --- Dynamics --- Machine theory --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers