Time-dependent partial differential equations and their numerical solution
著者
書誌事項
Time-dependent partial differential equations and their numerical solution
（Lectures in mathematics ETH Zürich）
Birkhäuser Verlag, c2001
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注記
Includes bibliographical references (p. [79]) and index
内容説明・目次
内容説明
This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions. The theoretical results are then applied to Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. This book will be a useful introduction to the field for applied mathematicians and graduate students.
目次
1 Cauchy Problems.- 1.1 Introductory Examples.- 1.2 Well-Posedness.- 1.3 Hyperbolic Systems with Constant Coefficients.- 1.3.1 In One Space Dimension.- 1.3.2 Symmetrizer.- 1.3.3 Multiple Space Dimensions.- 1.4 General Systems with Constant Coefficients.- 1.4.1 Parabolic Systems.- 1.4.2 Mixed Systems.- 1.5 Linear Systems with Variable Coefficients.- 1.6 Remarks.- 2 Half Plane Problems.- 2.1 Hyperbolic Systems in One Dimension.- 2.2 Hyperbolic Systems in Two Dimensions.- 2.3 Well-Posed Half Plane Problems.- 2.4 Well-Posed Problems in the Generalized Sense.- 2.5 Farfield Boundary Conditions.- 2.6 Energy Estimates.- 2.7 First Order Systems with Variable Coefficients.- 2.8 Remarks.- 3 Difference Methods.- 3.1 Periodic Problems.- 3.2 Half Plane Problems.- 3.2.1 Energy Estimates.- 3.2.2 Estimates by using Laplace Transform.- 3.2.3 Error Estimates.- 3.3 Method of Lines.- 3.4 Remarks.- 4 Nonlinear Problems.- 4.1 General Discussion.- 4.2 Initial Value Problems for Ordinary Differential Equations.- 4.3 Existence Theorems for Nonlinear Partial Differential Equations.- 4.4 Perturbation Expansion.- 4.5 Convergence of Difference Methods.- 4.6 Remarks.
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