Solving differential problems by multistep initial and boundary value methods
著者
書誌事項
Solving differential problems by multistep initial and boundary value methods
（Stability and control : theory, methods and applications, v. 6）
Gordon & Breach, c1998
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注記
Includes bibliographies and index
内容説明・目次
内容説明
The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.
目次
1. Differential Equations 2. Linear Difference Equations with Constant Coefficients 3. Polynomials and Toeplitz Matrices 4. Numerical Methods for Initial Value Problems 5. Generalized Backward Differentiation Formulae
6. Symmetric Schemes 7. Generalized Adams Methods 8. Hamiltonian Problems 9. Boundary Value Problems 10. Mesh Selection Strategies 11. Block BVMs 12. Parallel Implementation of B2VMs 13. Extensions and Applications to Special Problems
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