Stability of a second order of accuracy difference scheme for hyperbolic equation in a Hilbert space

Discrete Dynamics in Nature and Society

Volumn 2007, Issue 1, 2007, Pages

  Ashyralyev, Allaberen ^a   Koksal, Mehmet Emir ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 55249089454     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2007/57491     Document Type: Article

References (14)

1. H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, vol. 108 of North- Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 1985.
2. S. G. Kreǐn, Linear Differential Equations in a Banach Space, Nauka, Moscow, Russia, 1967.
3. A. Ashyralyev, "Difference schemes of a higher order of accuracy for second-order evolution equations," in Functional-Differential Equations (Russian), pp. 145-150, Perm Polytechnic Institute, Perm, Russia, 1989.
4. S. I. Piskarëv, "Approximation of holomorphic semigroups," Tartu Riikliku Ülikooli Toimetised, no. 492, pp. 3-14, 1979.
5. S. I. Piskarëv, "Stability of difference schemes in Cauchy problems with almost periodic solutions," Differentsial'nye Uravneniya, vol. 20, no. 4, pp. 689-695, 1984.
6. S. I. Piskarëv, "Principles of discretization methods III," Tech. Rep., Acoustic Institute, Academy of Science USSR, Moscow, Russia, 1986.
7. P. E. Sobolevskiľi and L. M. . Čebotareva, "Approximate solution of the Cauchy problem for an abstract hyperbolic equation by the method of lines," Izvestija Vysših Učebnyh Zavedeniǐ Matematika, no. 5(180), pp. 103-116, 1977 (Russian).
8. A. Ashyralyev and I. Muradov, "On one difference scheme of a second order of accuracy for hyperbolic equations," in Proceeding of the IMM of AS of Turkmenistan, pp. 58-63, Ashgabat, Turkmenistan, June 1995.
9. A. Ashyralyev and P. E. Sobolevskii, "A note on the difference schemes for hyperbolic equations," Abstract and Applied Analysis, vol. 6, no. 2, pp. 63-70, 2001.
10. A. Ashyralyev and P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, vol. 148 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 2004.
11. A. Ashyralyev and P. E. Sobolevskii, "Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations," Discrete Dynamics in Nature and Society, vol. 2005, no. 2, pp. 183-213, 2005.
12. A. Ashyralyev and M. E. Koksal, "On the second order of accuracy difference scheme for hyperbolic equations in a Hilbert space," Numerical Functional Analysis and Optimization, vol. 26, no. 7-8, pp. 739-772, 2005.
13. P. E. Sobolevskiǐ and V. A. Pogorelenko, "Hyperbolic equations in a Hilbert space," Sibirskiǐ Matematičeskiǐ Žurnal, vol. 8, pp. 123-145, 1967.
14. Yu. L. Daletskii, "Path integrals associated with the operator evolution equations," Uspekhi Matematicheskikh Nauk, vol. 17, no. 5, pp. 3-115, 1958.