Author | Ashyralyev, Allaberen. author |
---|---|
Title | New Difference Schemes for Partial Differential Equations [electronic resource] / by Allaberen Ashyralyev, Pavel E. Sobolevskii |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7922-4 |
Descript | IX, 446 p. online resource |
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 Taylorโs 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 Taylorโs 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 Taylorโs 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 Taylorโs 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 Taylorโs 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