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Numerical analysis --- Partial differential equations --- 519.63 --- Differential equations, Partial --- -Partial differential equations --- Numerical methods for solution of partial differential equations --- Numerical solutions --- Numerical solutions. --- -Numerical methods for solution of partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- -519.63 Numerical methods for solution of partial differential equations --- Calcul differentiel --- Solution numerique

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519.63 --- Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations. --- 519.63 Numerical methods for solution of partial differential equations --- Mathematics --- Math --- Science --- Computer programs.

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Fluid dynamics --- Mathematics. --- 519.63 --- 532.52 --- 532.52 Conditions of fluid motion --- Conditions of fluid motion --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Mathematics

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The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.

Numerical solutions of differential equations --- Differential equations, Partial --- Equations aux dérivées partielles --- Numerical solutions --- Solutions numériques --- 519.63 --- -Partial differential equations --- Numerical methods for solution of partial differential equations --- Numerical solutions. --- -Numerical methods for solution of partial differential equations --- -519.63 Numerical methods for solution of partial differential equations --- Partial differential equations --- Equations aux dérivées partielles --- Solutions numériques --- 519.63 Numerical methods for solution of partial differential equations --- Numerical analysis --- Mathematical analysis. --- Analysis (Mathematics). --- Numerical analysis. --- Partial differential equations. --- Analysis. --- Numerical Analysis. --- Partial Differential Equations. --- Mathematical analysis --- 517.1 Mathematical analysis --- Differential equations, Partial - Numerical solutions

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Bifurcation theory --- Stability --- Mathematical physics --- Théorie de la bifurcation --- Stabilité --- Physique mathématique --- 519.63 --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Physical mathematics --- Physics --- Differential equations, Nonlinear --- Numerical methods for solution of partial differential equations --- Mathematics --- Numerical solutions --- Bifurcation theory. --- Mathematical physics. --- Stability. --- 519.63 Numerical methods for solution of partial differential equations --- Théorie de la bifurcation --- Stabilité --- Physique mathématique