Taylor polynomial solution of hyperbolic type partial differential equations with constant coefficients

International Journal of Computer Mathematics

Volumn 88, Issue 3, 2011, Pages 533-544

  Bülbül, Berna ^a   Sezer, Mehmet ^a  

^a MUGLA SITKI KOCMAN UNIVERSITY   (Turkey)

Author keywords

double Taylor series; hyperbolic partial differential equations; Taylor matrix method; Taylor polynomial solutions

Indexed keywords

EID: 79251477204     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207161003611242     Document Type: Article

References (27)

1. A. Ashyralyev and M.E. Koksal, On the numerical solution of hyperbolic PDE with variable space operator, Numer. Methods Partial Diff. Equ. 25 (5) (2009), pp. 1086-1099.
2. A. Ashyralyev and M.E. Koksal, On the second order of accuracy difference scheme for hyperbolic equations in Hilbert space, Numer. Funct. Anal. Opt. 26 (2005), pp. 24-30.
3. A. Asyralyev and P.E. Sobolevskii, Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic partial differential equations, Discrete Dyn. Nat. Soc. 2 (2005), pp. 183-213.
4. J. Biazar and H. Ebrahimi, An approximation to the solution of hyperbolic equations by Adomian decomposition method and comparison with characteristic method, Appl. Math. Comput. 163 (2005), pp. 633-638. (Pubitemid 40219909)
5. M. Dehghan, On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation, Numer. Methods Partial Diff. Equ. 21 (2005), pp. 24-40.
6. M. Dehghan and M. Lakestani, The use of Chebyshev cardinal functions for solution of the second-Order onedimensional telegraph equation, Numer. Methods Partial Diff. Equ. 25 (4) (2009), pp. 931-938.
7. M. Dehghan and M. Lakestani, The use of cubic B-spline scaling functions for solving the one dimensional hyperbolic equation with nonlocal conservation condition, Numer. Methods Partial Diff. Equ. 23 (2007), pp. 1277-1289.
8. M. Dehghan and A. Shokri, A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions, Numer. Methods Partial Diff. Equ. 25 (2) (2009), pp. 494-506.
9. M. Dehghan and A. Shokri, A numerical method for solving the hyperbolic telegraph equation, Numer. Methods Partial Diff. Equ. 24 (4) (2008), pp. 1080-1093.
10. M.S. El-Azab and M. El-Gamel, A numerical algorithm for solution of telegraph equations, Appl. Math. Comput. 190 (2007), pp. 757-764.
11. D.J. Evans and H. Bulut, The numerical solution of the telegraph equation by the alternating group explicit (age) method, Int. J. Comput. Math. 80 (2003), pp. 1289-1297.
12. F. Gao and C. Chi, Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation, Appl. Math. Comput. 187 (2007), pp. 1272-1276.
13. D. Greenspan, Introduction to Partial Differential Equations, McGraw-Hill Company, New York, 1961.
14. M. Gülsu and M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math. 82 (5) (2005), pp. 629-642. (Pubitemid 41648294)
15. M. Gülsu and M. Sezer, On the solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007), pp. 446-449.
16. A. Karamete and M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79(9) (2002), pp. 987-1000.
17. N. Kurt and M. Çevik, Polynomial solution of the single degree of freedom system by Taylor matrix method, Mech. Res. Commun. 35 (2008), pp. 530-536.
18. N.Kurt and M. Sezer, Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients, J. Franklin Inst. 345 (2008), pp. 839-850.
19. R.K. Mohanty and M.K. Jain, An uncontionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation, Numer. Methods Partial Diff. Equ. 17 (2001), pp. 684-688.
20. R.K. Mohanty, M.K. Jain, and U. Arora, An unconditionally stable Adi method for the linear hyperbolic equation in three space dimensions, Int. J. Comput. Math. 79 (2002), pp. 133-142.
21. ̧ S. Nas, S. Yalçinba̧s, and M. Sezer, A method for approximate solution of the high-order linear Fredholm integrodifferential equations, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821-834.
22. M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Edu. Sci. Technol. 25(5) (1994), pp. 625-633.
23. M. Sezer, A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821-834.
24. M. Sezer, M. Gülsu, and B. Tanay, A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor polynomials, J. Franklin Inst. 343 (2006), pp. 647-659.
25. S.Yalçinba̧s, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equation, Appl. Math. Comput. 127 (2002), pp. 196-206.
26. S. Yalçinba̧s and M. Sezer, The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2000), pp. 291-308.
27. S.A. Yousefi, Legendre Multiwavelet Galerkin method for solving the hyperbolic Telegraph equation, Numer. Methods Partial Diff. Equ. 26 (3) (2010), pp. 535-543.