Quaternionic Analysis and Elliptic Boundary Value Problems
| Main Authors: | , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
1989, 1989
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| Edition: | 1st ed. 1989 |
| Series: | International Series of Numerical Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Quaternionic Analysis
- 1.1. Algebra of Real Quaternions
- 1.2. H-regular Functions
- 1.3. A Generalized LEIBNIZ Rule
- 1.4. BOREL-POMPEIU’s Formula
- 1.5. Basic Statements of H-regular Functions
- 2. Operators
- 2.3. Properties of the T-Operator
- 2.4. VEKUA’s Theorems
- 2.5. Some Integral Operators on the Manifold
- 3. Orthogonal Decomposition of the Space L2,H(G)
- 4. Some Boundary Value Problems of DIRICHLET’s Type
- 4.1. LAPLACE Equation
- 4.2. HELMHOLTZ Equation
- 4.3. Equations of Linear Elasticity
- 4.4. Time-independent MAXWELL Equations
- 4.5. STOKES Equations
- 4.6. NAVIER-STOKES Equations
- 4.7. Stream Problems with Free Convection
- 4.8. Approximation of STOKES Equations by Boundary Value Problems of Linear Elasticity
- 5. H-regular Boundary Collocation Methods
- 5.1. Complete Systems of H-regular Functions
- 5.2. Numerical Properties of H-complete Systems of H-regular Functions
- 5.3. Foundation of a Collocation Method with H-regular Functions for Several Elliptic Boundary Value Problems
- 5.4. Numerical Examples
- 6. Discrete Quaternionic Function Theory
- 6.1. Fundamental Solutions of the Discrete Laplacian
- 6.2. Fundamental Solutions of a Discrete Generalized CAUCHY-RIEMANN Operator
- 6.3. Elements of a Discrete Quaternionic Function Theory
- 6.4. Main Properties of Discrete Operators
- 6.5. Numerical Solution of Boundary Value Problems of NAVIER-STOKES Equations
- 6.6. Concluding Remarks
- References
- Notations