Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent ProblemsSIAM, 2007 M01 1 - 356 páginas This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. |
Contenido
OT98_ch10 | 201 |
OT98_ch11 | 233 |
OT98_appa | 245 |
OT98_appb | 259 |
OT98_appc | 269 |
OT98_appd | 285 |
OT98_appe | 311 |
OT98_bm | 329 |
Otras ediciones - Ver todas
Finite Difference Methods for Ordinary and Partial Differential Equations ... Randall J. LeVeque Vista previa limitada - 2007 |
Términos y frases comunes
accuracy advection equation algorithm analysis applied approach approximation arise behavior boundary conditions bounded called Chapter choose coefficient components compute consider consistent constant convergence decay defined definite depends derivative determine diagonal difference differential equations diffusion dimension direction discretization discussed eigenvalues eigenvectors elements estimate Euler exact example expect explicit exponential fact factor Figure find finite difference first order fixed Fourier function given gives global grid points growth heat equation hence initial data interpolation interval introduced iteration leads linear system matrix method nonlinear norm Note numerical numerical method obtain operator order accurate original particular polynomial possible powers practice problem relation requires root satisfied second order Section shown shows similar simply smooth solution solve space spectral stability region step stiff Suppose theorem true truncation error typically vector wave zero