International Journal of Information Technology and Computer Science(IJITCS)

ISSN: 2074-9007 (Print), ISSN: 2074-9015 (Online)

Published By: MECS Press

IJITCS Vol.3, No.4, Aug. 2011

Non-polynomial Spline Difference Schemes for Solving Second-order Hyperbolic Equations

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Li-Bin Liu,Yong Zhang,Huai-Huo Cao

Index Terms

Second-order hyperbolic equation; non-polynomial cubic spline; conditionally stable; finite difference scheme.


In this paper, a class of improved methods based on non-polynomial cubic splines in space and finite difference in time direction are constructed for the second-order hyperbolic equations with initial boundary value problems. Truncation error and stability analysis of the methods have been carried out. It is shown that by suitably choosing the parameters, many known methods can be derived from ours. We also obtain a new high accuracy scheme of , which is conditionally stable for .Finally, a numerical experiment is tested and results are compared with other published numerical solutions.

Cite This Paper

Li-Bin Liu, Yong Zhang, Huai-Huo Cao, "Non-polynomial Spline Difference Schemes for Solving Second-order Hyperbolic Equations", International Journal of Information Technology and Computer Science(IJITCS), vol.3, no.4, pp.43-49, 2011. DOI: 10.5815/ijitcs.2011.04.07


[1]M. Chawla, M.A. Al-Zanaidi, D. J. Evans, Generalized trapezoidal formulas for parabolic equations, Int. J. Comput. Math. 70 (1998) 429-443.

[2]U. Dale von Rosenberg, Methods for the Numberical Solution of Partial Differential Equations, American Elsevier Publishing Company, Inc., 1969.

[3]K. George, E.H. Twizell, Stable second-order finite-difference methods for linear initial-boundary-value problems, Appl. Math. Lett. 19 (2006) 146-154.

[4]R. Hiberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, fourthed., Pearson Prentice Hall, New Jersey, 2004.

[5]J. Rashidinia, R. Jalilian, V. Kazemi, Spline methods for the solutions of hyperbolic equations, Appl. Math. Comput. 190 (2007) 882-886.

[6]Tariq Aziz, Arshad Khan, Jalil Rashidinia, Spline methods for the solution of fourth-order parabolic partial differential equations, Appl. Math. Comput. 167 (2005) 153-166.

[7]S. Sallam, M. Naim Anwar, M.R. Abdel-Aziz, Unconditioally stalbe $C^1$-cubic spline collocation method for solving parabolic equations, Int. J. Comput. Math. 81 (2004) 813-821.

[8]J. Rashidinia, Applications of spline to numerical solution of differential equations, AMU India (1990), M.phil. Dissertation.

[9]J.J.H. Miller, On the location of zeros of certain classes of polynomials with application to numerical analysis, J. Inst. Math. Appls. 8 (1971) 394-406.