Solving Differential Equations by Multistep Initial and Boundary Value Methods

Front Cover
CRC Press, May 22, 1998 - Mathematics - 412 pages
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.
 

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Contents

Differential Equations
1
Linear Difference Equations with Constant Coefficients
15
Polynomials and Toeplitz Matrices
51
Notes
77
Generalized Backward Differentiation Formulae
121
Notes
140
Notes
157
Symmetric Schemes
159
Hamiltonian Matrices
358
Symplectic Matrices
360
B Answers to the Exercises
363
Chapter 2
364
Chapter 3
370
Chapter 4
373
Chapter 5
380
Chapter 6
382

Notes
183
Boundary Value Problems
213
Mesh Selection Strategies
237
Block BVMs
279
Parallel Implementation of B2VMs
301
Extensions and Applications to Special Problems
325
Functions of matrices
349
Mmatrices
353
The Kronecker Product
354
1 Use of Kronecker Product for Solving Matrix Equations
357
Chapter 7
384
Chapter 8
387
Chapter 9
390
Chapter 11
391
Chapter 12
392
Appendix A
394
Bibliography
399
Index
413
Copyright

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