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Computer-aided analysis of difference schemes for partial differential equations [[electronic resource] /] / Victor G. Ganzha, E.V. Vorozhtsov
| Computer-aided analysis of difference schemes for partial differential equations [[electronic resource] /] / Victor G. Ganzha, E.V. Vorozhtsov |
| Autore | Ganzha V. G (Victor Grigorʹevich), <1956-> |
| Pubbl/distr/stampa | New York, : John Wiley & Sons, Inc., c1996 |
| Descrizione fisica | 1 online resource (476 p.) |
| Disciplina |
515.353
515/.353 |
| Altri autori (Persone) | VorozhtsovE. V <1946-> (Evgenii Vasilʹevich) |
| Soggetto topico |
Differential equations, Partial - Numerical solutions - Data processing
Finite differences - Data processing |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-24272-5
9786613813848 1-118-03260-8 1-118-03085-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations; Contents; Preface; 1 The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials; 1.1 Preliminary Discussion of Stability and Approximation; 1.2 Computer Algebra Systems; 1.3 A Brief Review of the Contents of Chapters; 1.4 Stability, Approximation, and Convergence; 1.5 A Survey of Methods for the Stability Analysis of Difference Schemes; 1.5.1 Von Neumann Stability Analysis; 1.5.2 Differential Approximation Method; 1.5.3 Method of Frozen Coefficients
1.6 Algebraic Criteria for Localization of Polynomial Zeros1.6.1 Similarity and Dimensional Considerations; 1.6.2 Liénard-Chipart Criterion; 1.6.3 Generalized Routh-Hurwitz Problem for the Characteristic Polynomial; 1.7 Determination of the Maximal Time Step from Stability Analysis Results; 1.7.1 The Use of the Least Squares Method; 1.7.2 A Method Based on the Requirement of a Constant Volume of a Cell of a Spatial Computing Mesh; 1.7.3 The Use of the Tables of the Coordinates of Points of Stability Region Boundaries; 1.8 On the Choice of Nondimensional Complexes; 1.9 Bibliographical Notes 1.9.1 Historical Note on Stability Theories1.9.2 Application of Algebraic Criteria to Stability Analyses; 1.9.3 Use of Computer Algebra for the Automation of Certain Stages of the Stability Analyses; References; 2 Symbolic-Numerical Method for the Stability Investigation of Difference Schemes on a Computer; 2.1 General Structure of the Symbolic-Numerical Method; 2.2 The Case of Diagonalizable Amplification Matrices; 2.3 Scheme Checker; 2.4 Symbolic Stages of the Method; 2.5 Generation of a FORTRAN Program by Computer Algebra 2.6 Computation of the Coordinates of Points of a Stability Region Boundary2.6.1 Use of the Bisection Method; 2.6.2 Automatic Determination of the Number of Spectral Grid Points; 2.7 Improved Accuracy of Numerical Results; 2.7.1 Scaling in the Routh Algorithm; 2.7.2 Scaling in the Routh-Hurwitz Algorithm; 2.8 Examples of Stability Analyses of Difference Schemes for Equations of Hyperbolic Type; 2.8.1 Two-Step Richtmyer's Form of the Lax-Wendroff Scheme; 2.8.2 MacCormack Scheme for the Two-Dimensional Advection Equation; 2.8.3 Jameson's Schemes 2.9 Stability Analysis of the MacCormack Scheme for Two-Dimensional Euler Equations2.10 Stability Analysis of the MacCormack Scheme for Three-Dimensional Euler Equations; 2.11 Examples of Stability Analyses of Difference Schemes for Navier-Stokes Equations; 2.11.1 A Family of Schemes for One-Dimensional Navier-Stokes Equations; 2.11.2 Difference Schemes on Curvilinear Grids; References; 3 Application of Optimization Methods to the Stability Analysis of Difference Schemes; 3.1 Formulation of a Search for Stability Region Boundaries of Difference Schemes in Terms of Optimization Theory 3.1.1 The Case of One Nondimensional Complex |
| Record Nr. | UNINA-9910141014603321 |
Ganzha V. G (Victor Grigorʹevich), <1956->
|
||
| New York, : John Wiley & Sons, Inc., c1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer-aided analysis of difference schemes for partial differential equations [[electronic resource] /] / Victor G. Ganzha, E.V. Vorozhtsov
| Computer-aided analysis of difference schemes for partial differential equations [[electronic resource] /] / Victor G. Ganzha, E.V. Vorozhtsov |
| Autore | Ganzha V. G (Victor Grigorʹevich), <1956-> |
| Pubbl/distr/stampa | New York, : John Wiley & Sons, Inc., c1996 |
| Descrizione fisica | 1 online resource (476 p.) |
| Disciplina |
515.353
515/.353 |
| Altri autori (Persone) | VorozhtsovE. V <1946-> (Evgenii Vasilʹevich) |
| Soggetto topico |
Differential equations, Partial - Numerical solutions - Data processing
Finite differences - Data processing |
| ISBN |
1-282-24272-5
9786613813848 1-118-03260-8 1-118-03085-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations; Contents; Preface; 1 The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials; 1.1 Preliminary Discussion of Stability and Approximation; 1.2 Computer Algebra Systems; 1.3 A Brief Review of the Contents of Chapters; 1.4 Stability, Approximation, and Convergence; 1.5 A Survey of Methods for the Stability Analysis of Difference Schemes; 1.5.1 Von Neumann Stability Analysis; 1.5.2 Differential Approximation Method; 1.5.3 Method of Frozen Coefficients
1.6 Algebraic Criteria for Localization of Polynomial Zeros1.6.1 Similarity and Dimensional Considerations; 1.6.2 Liénard-Chipart Criterion; 1.6.3 Generalized Routh-Hurwitz Problem for the Characteristic Polynomial; 1.7 Determination of the Maximal Time Step from Stability Analysis Results; 1.7.1 The Use of the Least Squares Method; 1.7.2 A Method Based on the Requirement of a Constant Volume of a Cell of a Spatial Computing Mesh; 1.7.3 The Use of the Tables of the Coordinates of Points of Stability Region Boundaries; 1.8 On the Choice of Nondimensional Complexes; 1.9 Bibliographical Notes 1.9.1 Historical Note on Stability Theories1.9.2 Application of Algebraic Criteria to Stability Analyses; 1.9.3 Use of Computer Algebra for the Automation of Certain Stages of the Stability Analyses; References; 2 Symbolic-Numerical Method for the Stability Investigation of Difference Schemes on a Computer; 2.1 General Structure of the Symbolic-Numerical Method; 2.2 The Case of Diagonalizable Amplification Matrices; 2.3 Scheme Checker; 2.4 Symbolic Stages of the Method; 2.5 Generation of a FORTRAN Program by Computer Algebra 2.6 Computation of the Coordinates of Points of a Stability Region Boundary2.6.1 Use of the Bisection Method; 2.6.2 Automatic Determination of the Number of Spectral Grid Points; 2.7 Improved Accuracy of Numerical Results; 2.7.1 Scaling in the Routh Algorithm; 2.7.2 Scaling in the Routh-Hurwitz Algorithm; 2.8 Examples of Stability Analyses of Difference Schemes for Equations of Hyperbolic Type; 2.8.1 Two-Step Richtmyer's Form of the Lax-Wendroff Scheme; 2.8.2 MacCormack Scheme for the Two-Dimensional Advection Equation; 2.8.3 Jameson's Schemes 2.9 Stability Analysis of the MacCormack Scheme for Two-Dimensional Euler Equations2.10 Stability Analysis of the MacCormack Scheme for Three-Dimensional Euler Equations; 2.11 Examples of Stability Analyses of Difference Schemes for Navier-Stokes Equations; 2.11.1 A Family of Schemes for One-Dimensional Navier-Stokes Equations; 2.11.2 Difference Schemes on Curvilinear Grids; References; 3 Application of Optimization Methods to the Stability Analysis of Difference Schemes; 3.1 Formulation of a Search for Stability Region Boundaries of Difference Schemes in Terms of Optimization Theory 3.1.1 The Case of One Nondimensional Complex |
| Record Nr. | UNINA-9910830853503321 |
|
Ganzha V. G (Victor Grigorʹevich), <1956->
|
||
| New York, : John Wiley & Sons, Inc., c1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer-aided analysis of difference schemes for partial differential equations / / Victor G. Ganzha, E.V. Vorozhtsov
| Computer-aided analysis of difference schemes for partial differential equations / / Victor G. Ganzha, E.V. Vorozhtsov |
| Autore | Ganzha V. G (Victor Grigorʹevich), <1956-> |
| Pubbl/distr/stampa | New York, : John Wiley & Sons, Inc., c1996 |
| Descrizione fisica | 1 online resource (476 p.) |
| Disciplina | 515/.353 |
| Altri autori (Persone) | VorozhtsovE. V <1946-> (Evgenii Vasilʹevich) |
| Soggetto topico |
Differential equations, Partial - Numerical solutions - Data processing
Finite differences - Data processing |
| ISBN |
9786613813848
9781282242722 1282242725 9781118032602 1118032608 9781118030851 1118030850 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations; Contents; Preface; 1 The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials; 1.1 Preliminary Discussion of Stability and Approximation; 1.2 Computer Algebra Systems; 1.3 A Brief Review of the Contents of Chapters; 1.4 Stability, Approximation, and Convergence; 1.5 A Survey of Methods for the Stability Analysis of Difference Schemes; 1.5.1 Von Neumann Stability Analysis; 1.5.2 Differential Approximation Method; 1.5.3 Method of Frozen Coefficients
1.6 Algebraic Criteria for Localization of Polynomial Zeros1.6.1 Similarity and Dimensional Considerations; 1.6.2 Liénard-Chipart Criterion; 1.6.3 Generalized Routh-Hurwitz Problem for the Characteristic Polynomial; 1.7 Determination of the Maximal Time Step from Stability Analysis Results; 1.7.1 The Use of the Least Squares Method; 1.7.2 A Method Based on the Requirement of a Constant Volume of a Cell of a Spatial Computing Mesh; 1.7.3 The Use of the Tables of the Coordinates of Points of Stability Region Boundaries; 1.8 On the Choice of Nondimensional Complexes; 1.9 Bibliographical Notes 1.9.1 Historical Note on Stability Theories1.9.2 Application of Algebraic Criteria to Stability Analyses; 1.9.3 Use of Computer Algebra for the Automation of Certain Stages of the Stability Analyses; References; 2 Symbolic-Numerical Method for the Stability Investigation of Difference Schemes on a Computer; 2.1 General Structure of the Symbolic-Numerical Method; 2.2 The Case of Diagonalizable Amplification Matrices; 2.3 Scheme Checker; 2.4 Symbolic Stages of the Method; 2.5 Generation of a FORTRAN Program by Computer Algebra 2.6 Computation of the Coordinates of Points of a Stability Region Boundary2.6.1 Use of the Bisection Method; 2.6.2 Automatic Determination of the Number of Spectral Grid Points; 2.7 Improved Accuracy of Numerical Results; 2.7.1 Scaling in the Routh Algorithm; 2.7.2 Scaling in the Routh-Hurwitz Algorithm; 2.8 Examples of Stability Analyses of Difference Schemes for Equations of Hyperbolic Type; 2.8.1 Two-Step Richtmyer's Form of the Lax-Wendroff Scheme; 2.8.2 MacCormack Scheme for the Two-Dimensional Advection Equation; 2.8.3 Jameson's Schemes 2.9 Stability Analysis of the MacCormack Scheme for Two-Dimensional Euler Equations2.10 Stability Analysis of the MacCormack Scheme for Three-Dimensional Euler Equations; 2.11 Examples of Stability Analyses of Difference Schemes for Navier-Stokes Equations; 2.11.1 A Family of Schemes for One-Dimensional Navier-Stokes Equations; 2.11.2 Difference Schemes on Curvilinear Grids; References; 3 Application of Optimization Methods to the Stability Analysis of Difference Schemes; 3.1 Formulation of a Search for Stability Region Boundaries of Difference Schemes in Terms of Optimization Theory 3.1.1 The Case of One Nondimensional Complex |
| Record Nr. | UNINA-9911019983303321 |
|
Ganzha V. G (Victor Grigorʹevich), <1956->
|
||
| New York, : John Wiley & Sons, Inc., c1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||