On the Numerical Solution of Hyperbolic PDEs with Variable Space Operator

Numerical Methods for Partial Differential Equations

Volumn 25, Issue 5, 2009, Pages 1086-1099

  Ashyralyev, Allaberen ^a   Koksal, Mehmet Emir ^a,b,c  

^a FATIH UNIVERSITY   (Turkey)

^b GEBZE TECHNICAL UNIVERSITY   (Turkey)

^c HALIC UNIVERSITY   (Turkey)

Author keywords

Difference schemes; Hyperbolic equation; Matlab implementation; Numerical solution; Stability estimates

Indexed keywords

EID: 67849099054     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20388     Document Type: Article

References (15)

1. 1 S. G. Krein, Linear differential equations in a banach space, Nauka, Moskow, 1966 (in Russian).
2. 2 H. O. Fattorini, Second order linear differential equations in banach space, North‐Holland, Elsevier Science Publishers B.V., 1985.
3. 3 A. Ashyralyev and N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations, Numer Func Anal Opt 25 (2004), 439–462.
4. 4 A. Ashyralyev and P. E. Sobolevskii, Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations, Discrete Dyn Nat Soc 2 (2005), 183–213.
5. 5 A. Ashyralyev and M. E. Koksal, On the second order of accuracy difference scheme for hyperbolic equations in a Hilbert spcae, Numer Func Anal Opt 26 (2005), 739–772.
6. 6 M. Dehghan, On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation, Numer Methods Partial Differential Eq 21 (2005), 24–40.
7. 7 A. Ashyralyev and M. E. Koksal, Stability of a second order of accuracy difference scheme for hyperbolic equations in a Hilbert space, Discrete Dyn Nat Soc 1 (2007), 1–25.
8. 8 M. Dehghan and M. Lakestani, The use of cubic B‐spline scaling functions for solving the one‐dimensional hyperbolic equation with a nonlocal conservation condition, Numer Methods Partial Differential Eq 23 (2007), 1277–1289.
9. 9 M. Ramezani, M. Dehghan, and M. C. Razzaghi, Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition, Numer Methods Partial Differential Eq 24 (2008), 1–8.
10. 10 A. Ashyralyev and O. Yildirim, On multipoint nonlocal boundary value problems for hyperbolic differential and difference equations, Taiwan J Math 13 (2009), 22–41.
11. 11 A. A. Samarskii, I. P. Gavrilyuk, and V. L. Makarov, Stability and regularization of three‐level difference schemes with unbounded operator coefficients in Banach spaces, SIAM J Numer Anal 39 (2001), 708–723.
12. 12 S. Piskarev, Stability of difference schemes in Cauchy problems with almost periodic solutions, Differentsial'nye Uravneyia 20 (1984), 689–695.
13. 13 W. D. Li, Z. Z. Sun, and L. Zhao, An analysis of a high‐order difference scheme for numerical solution to u tt = A (x, t) u xx + F (x, t, u, u t, u x), Numer Methods Partial Differential Eq 23 (2007), 484–498.
14. 14 A. Ashyralyev and P. E. Sobolevskii, A note on the difference schemes for hyperbolic equations, Abstr Appl Anal 6 (2001), 63–70.
15. 15 P. E. Sobolevskii, Difference methods for the approximate solution of differential equations, Voronezh State University Press, Voronezh, 1975 (in Russian).