International Journal of Mathematics Trends and Technology
Volume 56 | Number 4 | Year 2018 | Article Id. IJMTT-V56P533 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P533
Three numerical method have been used to solve the one dimensional one way wave equation and second-order linear wave equation with constant coefficients. We discuss finite difference method for hyperbolic PDE. we consider the lax-wendroff scheme, the leapfrog scheme, upwind scheme finite difference scheme. We solve a one dimensional numerical experiment with specified initial and boundary condition, for which the exact solution is known using all these three schemes using some different values for the space and time step sizes denoted by h and k, respectively.
1. Richard L.Burden ,J. Douglas Faires “numerical analysis” in 9th edition.
2. Padul duchateau david w.zachmann schaum’s outline series thory and problems of “partial differential equation”.
3. John c. strikwerda, finite difference schemes and partial differential equation. Society for industrial and applied mathematics, Philadelphia, 2nd edition, 2004.
4.Randall J. Leveque , numerical methods for conservation laws. Springer basel AG, 2 nd edition, 1992.
5.M.LUKACOVA-MEDVID’OVA AND G.WARNECKE, lax wendroff type second order evolution galerkin method for multidimensional hyperbolic system, East -West J.NUMER.Math.,8(2000).
6. T.SCHWARTZKOPFF, C.D. MUNZ. AND E. F. TORO, ADER: a higer order approach for linear hyperbolic system in 2D, J. sci.comput., 17(2002),pp.231-240.
7.E. C. Zachmanoglou and D. W. Thoe. Introduction to paratial differential equatiation with applications. Dover publications,inc,1986.
8. A. Iserles. A first course in the numerical analysis of differential equation. Cambridge university press, 1996.
9.G. D. smith.numerical solution of paratial differential equations: finite difference methods. Oxfrod university press, third edition,1986.
10.R. D. Richtmyer and K. W.Morton. differene methods for initial- value problems. Interscience a division of John Wiley &Sons, Second edition, 1967.
11.R. J. Leveque. Finite difference methods for differential eauations-lecture notes URL=ftp://amath.washington.edu/pub/rjl/papers/amath58x.ps.gz.
12.P. D. Lax & B. WENDROFF, “difference scheme for hyperbolic equations with high order of accuracy,” comm.. pure appl. Math., v.17,1964, pp.381-398.MR 30#722.
13.L. L. Takacs, “a two step scheme for the advection equation with minimized dissipation and dispersion error,” monthly weather review, vol.113, no.6,pp.1050-1065,1985.
14.J. E. Fromm, “a method for reducing dispersion in convective difference schemes,” journal of computational physis, vol.3, no.2,pp.176-189,1968.
15. K. W. Morton and D. F. Mayers, numerical solution of paratial differential equations, Cambridge university press, cambridgr UK, 1994.
16. R. J.Babarsky and R.Sharpley, “expanded stability through higer temporal accuracy for time-centered advection schemes,” monthly weather review, vol. 125, no.6, pp.1277-1295, 1997.
17.V. GUVANASEN and R.E.VOLKER, “Numerical solutions for solute transport in unconfined aquifers.” International Journals for Numerical Methods in fluids,vol.3,no.2,pp.103-123,1983.
18.M. Dehghan. “On the numerical solution of the one- dimensional convection-diffusion equation,” Mathematical problems in Engineering,vol. 2005, no. 1,pp. 61-74,2005.
19.R.Smith and Y. Tang,”Optimal and near-optimal advection diffusion finite-difference schemes. V. Error propagation.” Proceedings of the The Royal society of London A, vol. 457, no. 2008 pp.803- 816,2001.
20. C.Hirsch, Numerical Computation of Internal and External Flows, vol. 1,John Wiley & Sons, New York, NY, USA,1988.
Dr.S. Karunanithi, M. Malarvizhi, N. gajalakshmi, M. lavanya, "A Study on FDM of Hyperbolic PDE in Comparative of Lax-Wendroff, Upwind, Leapfrog Methods on Numerical Analysis," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 4, pp. 229-235, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P533
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