New Difference Schemes for Partial Differential Equations
Springer Basel (Verlag)
978-3-7643-7054-1 (ISBN)
The book will be of value for professional mathematicians as well as for advanced students in the fields of numerical analysis, functional analysis, and differential equations.
1 Linear Difference Equations.- 1.1 Difference Equations of the First Order.- 1.2 Difference Equations of the Second Order.- 1.3 Difference Equations with Constant Coefficients.- 2 Difference Schemes for First-Order Differential Equations.- 2.1 Single-Step Exact Difference Scheme and Its Applications.- 2.2 Taylor’s Decomposition on Two Points and Its Applications.- 3 Difference Schemes for Second-Order Differential Equations.- 3.1 Two-Step Exact Difference Scheme and Its Applications.- 3.2 Taylor’s Decomposition on Three Points and Its Applications.- 4 Partial Differential Equations of Parabolic Type.- 4.1 A Cauchy Problem. Well-posedness.- 4.2 Difference Schemes Generated by an Exact Difference Scheme.- 4.3 Single-Step Difference Schemes Generated by Taylor’s Decomposition.- 5 Partial Differential Equations of Elliptic Type.- 5.1 A Boundary-Value Problem. Well-posedness.- 5.2 Difference Schemes Generated by an Exact Difference Scheme.- 5.3 Two-Step Difference Schemes Generated by Taylor’s Decomposition.- 6 Partial Differential Equations of Hyperbolic Type.- 6.1 A Cauchy Problem.- 6.2 Difference Schemes Generated by an Exact Difference Scheme.- 6.3 Two-Step Difference Schemes Generated by Taylor’s Decomposition.- 7 Uniform Difference Schemes for Perturbation Problems.- 7.1 A Cauchy Problem for Parabolic Equations.- 7.2 A Boundary-Value Problem for Elliptic Equations.- 7.3 A Cauchy Problem for Hyperbolic Equations.- 8 Appendix: Delay Parabolic Differential Equations.- 8.1 The Initial-Value Differential Problem.- 8.2 The Difference Schemes.- Comments on the Literature.
Erscheint lt. Verlag | 25.6.2004 |
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Reihe/Serie | Operator Theory: Advances and Applications |
Zusatzinfo | IX, 446 p. |
Verlagsort | Basel |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 975 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Schlagworte | Boundary value problem • Functional Analysis • hyperbolic equation • Numerical analysis • Numerische Analysis • Operatortheorie • partial differential equation • Partial differential equations • Partielle Differentialgleichungen • Partielle Differenzialgleichungen |
ISBN-10 | 3-7643-7054-8 / 3764370548 |
ISBN-13 | 978-3-7643-7054-1 / 9783764370541 |
Zustand | Neuware |
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