Author | Deuflhard, Peter. author |
---|---|
Title | Scientific Computing with Ordinary Differential Equations [electronic resource] / by Peter Deuflhard, Folkmar Bornemann |
Imprint | New York, NY : Springer New York, 2002 |
Connect to | http://dx.doi.org/10.1007/978-0-387-21582-2 |
Descript | XX, 486 p. online resource |
1 Time-Dependent Processes in Science and Engineering -- 1.1 Newtonโs Celestial Mechanics -- 1.2 Classical Molecular Dynamics -- 1.3 Chemical Reaction Kinetics -- 1.4 Electrical Circuits -- Exercises -- 2 Existence and Uniqueness for Initial Value Problems -- 2.1 Global Existence and Uniqueness -- 2.2 Examples of Maximal Continuation -- 2.3 Structure of Nonunique Solutions -- 2.4 Weakly Singular Initial Value Problems -- 2.5 Singular Perturbation Problems -- 2.6 Quasilinear Differential-Algebraic Problems -- Exercises -- 3 Condition of Initial Value Problems -- 3.1 Sensitivity Under Perturbations -- 3.2 Stability of ODEs -- 3.3 Stability of Recursive Mappings -- Exercises -- 4 One-Step Methods for Nonstiff IVPs -- 4.1 Convergence Theory -- 4.2 Explicit Runge-Kutta Methods -- 4.3 Explicit Extrapolation Methods -- 5 Adaptive Control of One-Step Methods -- 5.1 Local Accuracy Control -- 5.2 Control-Theoretic Analysis -- 5.3 Error Estimation -- 5.4 Embedded Runge-Kutta Methods -- 5.5 Local Versus Achieved Accuracy -- Exercises -- 6 One-Step Methods for Stiff ODE and DAE IVPs -- 6.1 Inheritance of Asymptotic Stability -- 6.2 Implicit Runge-Kutta Methods -- 6.3 Collocation Methods -- 6.4 Linearly Implicit One-Step Methods -- Exercises -- 7 MultiStep Methods for ODE and DAE IVPs -- 7.1 Multistep Methods on Equidistant Meshes -- 7.2 Inheritance of Asymptotic Stability -- 7.3 Direct Construction of Efficient Multistep Methods -- 7.4 Adaptive Control of Order and Step Size -- Exercises -- 8 Boundary Value Problems for ODEs -- 8.1 Sensitivity for Two-Point EVPs -- 8.2 Initial Value Methods for Timelike EVPs -- 8.3 Cyclic Systems of Linear Equations -- 8.4 Global Discretization Methods for Spacelike EVPs -- 8.5 More General Types of BVPs -- 8.6 Variational Problems -- Exercises -- References -- Software