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MARC 21

Time-dependent Partial Differential Equations and Their Numerical Solution
Tag	Description
020	$a9783034882293
082	$a515
099	$aOnline resource : Birkhäuser
100	$aKreiss, Heinz-Otto.
245	$aTime-dependent Partial Differential Equations and Their Numerical Solution$h[EBook]$cby Heinz-Otto Kreiss, Hedwig Ulmer Busenhart.
260	$aBasel$bBirkhäuser$c2001.
300	$aVIII, 82 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aLectures in Mathematics. ETH Zürich, Department of Mathematics Research Institute of Mathematics
505	$a1 Cauchy Problems -- 1.1 Introductory Examples -- 1.2 Well-Posedness -- 1.3 Hyperbolic Systems with Constant Coefficients -- 1.4 General Systems with Constant Coefficients -- 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 -- 3.3 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.
520	$aIn these notes we study time-dependent partial differential equations and their numerical solution. The analytic and the numerical theory are developed in parallel. For example, we discuss well-posed linear and nonlinear problems, linear and nonlinear stability of difference approximations and error estimates. Special emphasis is given to boundary conditions and their discretization. We develop a rather general theory of admissible boundary conditions based on energy estimates or Laplace transform techniques. These results are fundamental for the mathematical and numerical treatment of large classes of applications like Newtonian and non-Newtonian flows, two-phase flows and geophysical problems.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aBusenhart, Hedwig Ulmer.$eauthor.
710	$aSpringerLink (Online service)
830	$aLectures in Mathematics. ETH Zürich, Department of Mathematics Research Institute of Mathematics
856	$uhttp://dx.doi.org/10.1007/978-3-0348-8229-3