Author | Kreiss, Heinz-Otto. author |
---|---|
Title | Time-dependent Partial Differential Equations and Their Numerical Solution [electronic resource] / by Heinz-Otto Kreiss, Hedwig Ulmer Busenhart |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8229-3 |
Descript | VIII, 82 p. online resource |
1 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