HAAR WAVELET AND ADOMAIN DECOMPOSITION METHOD FOR THIRD ORDER PARTIAL DIFFERENTIAL EQUATIONS ARISING IN IMPULSIVE MOTION OF A AT PLATE
Subject Areas : International Journal of Mathematical Modelling & Computations
1 - Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology,
Jalandhar, Punjab-144011, India
2 - Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology,
Jalandhar, Punjab-144011, India
Keywords: Haar wavelet, Operational matrix, Linear third order partial differential equation, Adomain decomposition method,
Abstract :
We present here, a Haar wavelet method for a class of third order partial dierentialequations (PDEs) arising in impulsive motion of a flat plate. We also, present Adomaindecomposition method to find the analytic solution of such equations. Efficiency andaccuracy have been illustrated by solving numerical examples.
R.A. Van Gorder, K. Vajravelu, Third-order partial differential equations arising in the impulsive motion of a at plate, Commun. Nonlinear Sci. Numer. Simul. 14 (6) (2009) 2629{2636.
A.M. Wazwaz, An analytic study on the third-order dispersive partial differential equations, Appl. Math. Comput. 142 (2) (2003) 511-520.
A.M. Wazwaz, Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations, Appl. Math. Comput. 195 (2) (2008) 754-761.
M. Mechee, F. Ismail, Z.M. Hussain, Z. Siri, Direct numerical methods for solving a class of third-order partial differential equations, Applied Mathematics and Computation 247 (2014) 663-674.
I. Teipel, The impulsive motion of a at plate in a viscoelastic
uid. Acta Mech 39 (1981) 277-9.
C.F. Chen, C.H. Hsiao, Haar wavelet method for solving lumped and distributed parameter systems, IEE. Proc. Control Theory Appl. 144 (1997) 87-94.
U. Lepik, Numerical solution of evolution equations by the Haar wavelet method, Applied Mathematics and Computation 185 (2007) 695 -704.
U. Lepik, Numerical solution of dierential equations using Haar wavelets, Math. Comput. Simul. 68 (2005) 127-143.
U. Lepik, Application of the Haar wavelet transform for solving integral and differential equations, Proc. Estonian Acad. Sci. Phys. Math. 56 (1) (2007) 28-46.
I. Celik, Haar wavelet method for solving generalized BurgersHuxley equation, Arab Journal of Mathematical Sciences 18 (2012), 25-37.
G. Hariharan, K. Kannan, K.R. Sharma, Haar wavelet method for solving Fishers equation, Appl. Math. Comput. 211 (2009) 284-292.
G. Hariharan, K. Kannan, Haar wavelet method for solving FitzHugh-Nagumo equation, Int. J. Math. Stat. Sci. 2(2) (2010) 59-63.
A. Haar, Zur theorie der orthogonalen Funktionsysteme, Math. Annal. 69 (1910) 331-71.
G.B. Whitham, Linear and nonlinear waves, Wiley, New York, 1974.
G. Adomian, Solving Frontier Problems of Physics: The Decomposition Methods, Kluwer Academic Publishers, Boston (1994).