Determination of two-time dependent coefficients in a parabolic partial differential equation by homotopy analysis method

Authors

  • Ogugua Onyejekwe Eastern Florida State College

DOI:

https://doi.org/10.14419/ijamr.v3i2.2219

Published:

2014-04-15

Abstract

In this paper the solution procedure in obtaining two times - dependent coefficients in a one dimensional partial differential equation and the temperature distribution is discussed and solved. We use the homotopy analysis method to obtain the solution of both the unknown coefficients and the temperature distribution.  The solutions to the unknown coefficients are obtained by reducing our problem to a system of equations at every time step. There are advantages to using HAM, firstly it is independent of small/large physical parameters, there is flexibility on the choice of base function and initial guess of solution and lastly there is great generality. The results obtained from this method shows high accuracy, computational efficiency and a strong rate of convergence.

 

Keywords: Heat Equation, Homotopy Analysis Method, Inverse Problem, Time - Dependent Diffusion Coefficients.

References

A.G. Fatullayev, “Numerical procedure for the simultaneous determination of unknown coefficients in a parabolic equation”, Appl. Math. Compute 162(2005), 1367 -1375.

A.K. Alomari, “Modifications of Homotopy Analysis Method for Differential Equations: Modifications of Homotopy Analysis Method, Ordinary, Fractional, Delay, and Algebraic Equations”, Lambert Academic Publishing, Germany, 2012.

A. Saadatmandi, M.Deghan, “Computation of two time-dependent coefficients in a parabolic partial differential equation subject to additional specifications”, International Journal of Computer Mathematics, 85(2010), 997-1008.

J.R. Cannon, Y.Lin and S.Xu, “Numerical procedure for the determination of an unknown coefficient in semilinear parabolic equations”, Inv. Probl, 10(1994), 227-243.

O.N.Onyejekwe, “Solution of some parabolic inverse problems by homotopy analysis method”, International Journal of Applied Mathematical Research, 3(2014), pp.81-87.

S. Liao, “Homotopy Analysis Method in Nonlinear Equations”, Springer, New York, 2012.

S. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method”, Chapman & Hall/CRC, 2004.

S. Liao, “Notes on the homotopy analysis method – Some definitions and theorems”, Common, Nonlinear Sci. Numer. Simulat, 14(2009), pp.983 – 997.

View Full Article: