Septic B-spline Collocation Method for Solving One-dimensional Hyperbolic Telegraph Equation
Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331893Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1335
 D. M. Pozar, Microwave Engineering. NewYork: Addison-Wesley, 1990.
 A. Mohebbi, M. Dehghan, High order compact solution of the one-spacedimensional linear hyperbolic equation, Numerical Methods for Partial Differential Equations, 24 (2008) 1222-1235.
 A. Jeffrey, Advanced Engineering Mathematics. Harcourt Academic Press, 2002.
 A. Jeffrey, Applied Partial Differential Equations. NewYork: Academic Press, 2002.
 R. K. Mohanty, New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations, Computer Mathematics, 86 (2008) 2061 - 2071.
 H. Pascal, Pressure wave propagation in a fluid flowing through a porous medium and problems related to interpretation of Stoneley-s wave attenuation in acoustical well logging, Engineering Science, 24 (1986) 1553-1570.
 G. Bohme, Non-Newtonian Fluid Mechanics, NewYork: North-Holland, 1987.
 D. J. Evans, H. Bulut, Thenumerical solution of thetelegraph equation by the alternating group explicit method, Computer Mathematics, 80 (2003) 1289- 1297.
 P. M. Jordan, M. R. Meyer, A. Puri, Causal implications of viscous damping in compressible fluid flows. Phys Rev, 62 (2000) 7918-7926.
 L. L. Schumaker, Spline Functions: Basic Theory, Krieger Publishing Company, Florida, 1981.
 J. M. Ahlberg, E. N. Nilson, J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, NewYork, 1967.
 P. M. Prenter, Splines and Variational Methods, New York: John Wiley, 1975.
 C. De Boor, A Practical Guide to Splines, Springer-Verlag, New York, 1978.
 G. Micula, Handbook of Splines, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
 M. A. Ramadan, T. S. El-Danaf, F. E.I. Abd Alaal, A numerical solution of the Burgers- equation using septic B-splines, Chaos, Solitons and Fractals, 26 (2005) 795-804.
 T. S. A. El-Danaf, Septic B-spline method of the Korteweg-de Vries- Burger-s equation, Communications in Nonlinear Science and Numerical Simulation, 13 (2008) 554-566.
 A. A. Soliman, M. H. Hussien, Collocation solution for RLW equation with septic spline, Applied Mathematics and Computation, 161 (2005) 623-636.
 A.Quarteroni, R. Sacco, F. Saleri, Numerical mathematics, Springer- Verlag, Berlin, 2007.