Author | Marchuk, G. I. author |
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Title | Difference Methods and Their Extrapolations [electronic resource] / by G. I. Marchuk, V. V. Shaidurov |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8224-9 |
Descript | 334p. online resource |
1 General Properties -- 1.1. The Simplest Example -- 1.2. Expansion Theorems -- 1.3. Acceleration of Convergence -- 1.4. Correction by Higher-Order Differences -- 1.5. Various Extrapolation Methods -- 1.6. The Effects of Computational Errors -- 2 First-Order Ordinary Differential Equations -- 2.1. The Crank-Nicholson Scheme -- 2.2. Explicit Difference Schemes -- 2.3. The Splitting-Up Method for Systems of Equations -- 2.4. Equations with Singularities -- 3 The One-Dimensional Stationary Diffusion Equation -- 3.1. The Dirichlet Problem -- 3.2. Boundary-Value Problems of the Third Kind -- 3.3. Equations with Discontinuous Coefficients -- 3.4. The Sturm-Liouville Problem -- 3.5. Improving the Accuracy of the Finite Elements Method -- 3.6. The Quasilinear Problem -- 4 Elliptic Equations -- 4.1. The Statement of the Problem -- 4.2. Difference Methods for the Dirichlet Problem on a Domain with a Smooth Boundary -- 4.3. The Dirichlet Problem in a Rectangle -- 4.4. A Quasilinear Equation in a Triangular Region -- 4.5. On the Diffraction Problem -- 4.6. On the Separation of Singularities -- 5 Nonstationary Problems -- 5.1. The Simplest Type of Parabolic Equation -- 5.2. Increasing the Accuracy of the Splitting-Up Method -- 5.3. The Two-Dimensional Heat Equation -- 5.4. The Equation of Motion -- 6 Extrapolation for Algebraic Problems and Integral Equations -- 6.1. Regularization of a Singular System of Linear Algebraic Equations -- 6.2. Regularization of a System with a Selfadjoint Matrix -- 6.3. Extrapolation of Solutions Containing Boundary-Layer Functions -- 6.4. The Fredholm Equation of the Second Kind -- 6.5. The Volterra Equation of the Second Kind -- 6.6. The Volterra Equation of the First Kind -- 7 Appendix -- 7.1. Expansion of Difference Relations in the Mesh-Size -- 7.2. On the Solution of Some Special Systems of Equations -- 7.3. Some Results on the Lagrange Interpolation Polynomials -- List of Notation