Numerical Methods for Evolutionary Differential EquationsSIAM, 01.01.2008 - 408 Seiten Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method. |
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CS05_ch2 | 37 |
CS05_ch3 | 91 |
CS05_ch4 | 135 |
CS05_ch5 | 151 |
CS05_ch6 | 181 |
CS05_ch7 | 211 |
CS05_ch8 | 253 |
CS05_ch9 | 275 |
CS05_ch10 | 327 |
CS05_ch11 | 365 |
CS05_bm | 375 |
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Numerical Methods for Evolutionary Differential Equations Uri M. Ascher Eingeschränkte Leseprobe - 2008 |
Häufige Begriffe und Wortgruppen
accuracy advection equation algebraic amplification applied approximate solution artificial backward Euler boundary conditions box scheme CFL condition Chapter computational conservation laws consider constant coefficient corresponding defined derivatives differential dimensions discontinuities dissipative domain eigenvalues exact solution Example Exercise explicit Figure finite difference finite element finite volume first order fixed flow flux formula Fourier Hamiltonian system heat equation higher order hyperbolic initial value initial value problem integration interpolation iteration KdV equation l2-norm Lax—Friedrichs scheme Lax—Wendroff scheme leapfrog scheme linear matrix mesh mesh function mesh points midpoint method multigrid nonlinear norm numerical obtain ODE system order accurate order method parabolic parameter polynomial polynomial interpolation preconditioner Runge—Kutta methods satisfies scalar second order Section semi-discretization significantly simple smooth solve space variables Specifically spectral methods splitting methods step stiff sufficiently symmetric positive definite symplectic method transform trapezoidal method truncation error upwind scheme value ODE value problem vector wave equation yields