Numerical Methods for Grid Equations

Inhaltsverzeichnis

• 5 The Mathematical Theory of Iterative Methods.
• 5.1 Several results from functional analysis.
• 5.2 Difference schemes as operator equations.
• 5.3 Basic concepts from the theory of iterative methods.
• 6 Two-Level Iterative Methods.
• 6.1 Choosing the iterative parameters.
• 6.2 The Chebyshev two-level method.
• 6.3 The simple iteration method.
• 6.4 The non-self-adjoint case. The simple iteration method.
• 6.5 Sample applications of the iterative methods.
• 7 Three-Level Iterative Methods.
• 7.1 An estimate of the convergence rate.
• 7.2 The Chebyshev semi-iterative method.
• 7.3 The stationary three-level method.
• 7.4 The stability of two-level and three-level methods relative to a priori data.
• 8 Iterative Methods of Variational Type.
• 8.1 Two-level gradient methods.
• 8.2 Examples of two-level gradient methods.
• 8.3 Three-level conjugate-direction methods.
• 8.4 Examples of the three-level methods.
• 8.5 Accelerating the convergence of two-level methods in the self-adjoint case.
• 9 Triangular Iterative Methods.
• 9.1 The Gauss-Seidel method.
• 9.2 The successive over-relaxation method.
• 9.3 Triangular methods.
• 10 The Alternate-Triangular Method.
• 10.1 The general theory of the method.
• 10.2 Boundary-value difference problems for elliptic equations in a rectangle.
• 10.3 The alternate-triangular method for elliptic equations in arbitrary regions.
• 11 The Alternating-Directions Method.
• 11.1 The alternating-directions method in the commutative case.
• 11.2 Sample applications of the method.
• 11.3 The alternating-directions method in the general case.
• 12 Methods for Solving Equationswith Indefinite and Singular Operators.
• 12.1 Equations with real indefinite operators.
• 12.2 Equations with complex operators.
• 12.3 General iterative methods for equations with singular operators.
• 12.4Special methods.
• 13 Iterative Methods for Solving Non-Linear Equations.
• 13.1 Iterative methods. The general theory.
• 13.2 Methods for solving non-linear difference schemes.
• 14 Example Solutions of Elliptic Grid Equations.
• 14.1 Methods for constructing implicit iterative schemes.
• 14.3 Systems of elliptic equations.
• 14.4 Methods for solving elliptic equations in irregular regions.
• 15 Methods for Solving Elliptic Equationsin Curvilinear Orthogonal Coordinates.
• 15.1 Posing boundary-value problems for differential equations.
• 15.2 The solution of difference problems in cylindrical coordinates.
• 15.3 Solution of difference problems in polar coordinate systems.
• Appendices.
• Construction of the minimax polynomial.
• Translator’s note.