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Differential equations, Partial --- 517.91 --- Numerical solutions --- Data processing --- Numerical solutions --- Numerical solutions --- Data processing --- MATLAB.
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This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.
Differential equations, Partial --- Numerical analysis --- Numerical solutions.
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Differential equations --- Numerical analysis. --- Numerical solutions.
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Eigenfunctions. --- Eigenvalues. --- Sturm-Liouville equation --- Numerical solutions.
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This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. With this new notio
Bifurcation theory. --- Differential equations, Nonlinear --- Numerical analysis --- Stability --- Numerical solutions. --- Numerical solutions
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This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
Differential equations, Partial --- Finite element method. --- Fluid dynamics. --- Numerical solutions.
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Differential equations --- Numerical solutions. --- 517.91 Differential equations
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Differential equations, Partial --- Finite element method. --- Numerical solutions.
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