Introduction / 1.: |
Two-Level Difference Schemes / 2.: |
Stability of Difference Schemes |
Canonical Form / 2.1: |
General Concept of Stability / 2.2: |
[rho]-Stability of Difference Schemes / 2.3: |
Conditions of Stability with Respect to the Initial Data / 3.: |
Stability in the Space H[subscript A] / 3.1: |
Stability in the Space H[subscript B] / 3.2: |
Condition for [rho]-Stability / 3.3: |
Stability of Schemes with Weights / 3.4: |
Stability with Respect to the Right Hand Side / 4.: |
Elementary Estimates in H[subscript A], H[subscript B] / 4.1: |
Splitting off the Stationary Non-Homogeneity / 4.2: |
A Priori Estimates for Stability under More Severe Restrictions / 4.3: |
Schemes with Weights / 4.4: |
Coefficient Stability / 5.: |
Strong Stability of Operator-Differential Schemes / 5.1: |
Strong Stability of the Operator-Difference Schemes / 5.2: |
Difference Schemes with Operator Factors |
Schemes with B = E + [tau]GA |
Stability with Respect to the Initial Data |
The Stability in Other Norms |
Schemes with B = E + [tau]AG |
Estimates of Stability with Respect to the Initial Data |
A Priori Estimates in Other Norms |
Difference Schemes with B = E + [tau]T*GT |
Estimates of Stability with Respect to the Right Hand Side |
Some Other A Priori Estimates |
Three-Level Difference Schemes |
Reduction to Two-Level Scheme |
Necessary and Sufficient Conditions |
[rho]-Stability |
Stability in Simpler Norms |
A Priori Estimates |
Stability for Homogeneous Initial Data |
Schemes with Variable Operators |
Stability in Other Norms |
Schemes for First-Order Evolutionary Equations |
Schemes with Weights for Second-Order Evolutionary Equations |
Three-Level Schemes with Operator Factors |
Schemes with D = E + 0.5[tau superscript 2]G[subscript 1]A, B = [tau]G[subscript 2]A |
Other A Priori Estimates |
Schemes with D = E + 0.5[tau superscript 2] AG[subscript 1], B = [tau]AG[subscript 2] |
Estimates of Stability with Respect to Initial Data |
Difference Schemes of Divergent Form |
Difference Schemes for Non-Stationary Equations / 6.: |
Boundary Problems for Parabolic Equations |
Difference-Differential Problem |
Stability Conditions |
Convergence of Difference Schemes / 2.4: |
Equation with Discontinuous Coefficients / 2.5: |
Multi-dimensional Problems / 2.6: |
Problems with Generalized Solutions |
Stability in Integral with Respect to Time Norms |
A Differential Problem |
Difference Scheme |
Approximation Error and Convergence |
Difference Schemes for Non-stationary Convection-Diffusion Problems |
Model Convection-Diffusion Problems |
The Stability of the Solution for the Continuous Problem |
Difference Operators of Convection and Diffusion |
Difference Schemes for Non-Stationary Problems / 4.5: |
Korteweg-de Vries Equation |
Formulation of the Problem and Basic Properties of Its Solution |
A Model Equation / 5.3: |
Schemes with Weighting Factors / 5.4: |
Nonlinear Schemes / 5.6: |
Implicit Conservative Schemes / 5.7: |
A Boundary Value Problem for a Hyperbolic Equation of the Second Order |
Difference Schemes / 6.1: |
An Approximation Error and Convergence / 6.3: |
Problems with Piecewise Smooth Solutions / 6.4: |
A Multi-dimensional Degenerative Equation with Dissipation / 6.5: |
Hyperbolo Parabolic Problems / 7.: |
Statement of the Problem / 7.1: |
Stability of the Difference Schemes with Constant Weights / 7.2: |
Difference Schemes with Variable Weighting Factors / 7.4: |
Truncation Error and Convergence / 7.5: |
Schemes on Adaptive Grids |
Difference Schemes on Grids Adaptive in Time for a Parabolic Equation |
Non-Conservative Schemes |
Conservative Schemes |
Difference Schemes for a Problem with Weak Solutions |
Difference Schemes for Multi-dimensional Equations |
Schemes with Adaptation with Respect to Time for a Wave Equation |
Stability and Convergence |
Difference Schemes of Domain Decomposition on the Grids Locally Refined with Respect to Time |
Model Problem |
Decomposition Operators |
Stability |
Difference Schemes on Dynamical Grids Locally Refined in Space |
Construction of a Scheme with New Nodes on the Upper Level |
Convergence |
Other Type of Interpolation |
The Case of Variable Coefficients |
Schemes of High Order of Approximation on Grids Non-Uniform with Respect to Space |
Difference Schemes for a Parabolic Equation |
Difference Schemes for a Hyperbolic Equation |
Difference Schemes for a Two-Dimensional Parabolic Equation |
Difference Schemes of Domain Decomposition for Non-Stationary Problems / 8.: |
Methods of Domain Decomposition |
Domain Decomposition |
Iterative Difference Schemes |
Schemes of Splitting with Respect to Spatial Variables |
Regionally Additive Schemes of Two-Component Splitting |
Problem Statement |
Difference Operators of Domain Decomposition |
Accuracy of Difference Solution |
Factorized Schemes of Domain Decomposition / 3.5: |
Regionally Additive Schemes of Summarized Approximation |
Regionally Additive Schemes |
Convergence of Schemes of Decomposition |
Vector Additive Schemes of Domain Decomposition |
Vector Scheme |
Convergence of the Scheme of Decomposition |
Other Decomposition Operators |
Schemes of Second-Order Approximation with Respect to Time |
Schemes of Domain Decomposition for Second-Order Evolutionary Equations |
Vector Problem |
Difference Schemes with Weights |
Additive Schemes |
Stability of Additive Schemes / 6.6: |
The Wave Equation / 6.7: |
References |
Index |
Introduction / 1.: |
Two-Level Difference Schemes / 2.: |
Stability of Difference Schemes |
Canonical Form / 2.1: |
General Concept of Stability / 2.2: |
[rho]-Stability of Difference Schemes / 2.3: |