2836-7863ISSN (Online)
Volume 3 , Issue 2 , PP: 18-24, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Murat Ozcek 1 *
Doi: https://doi.org/10.54216/NIF.030203
We studied the stability of the steady state solutions for Fisher Equation in two cases, the First one with constant amplitude and we show that the steady state solution u1=1 is always stable under any condition, but the other two solutions u1=0 and u1 (x)=A cos (nπX)are conditionally stable. In the Second case, we studied the steady state solutions for various amplitude by using two Methods. The First is analytically by direct Method and the second is numerical method using Galerkin technique which shows the same results, that is the steady state solution u1=1 is always stable under any conditions, but the other two solutions u1=0 and u1 (x)=A cos (nπX) are conditionally stable.
Galrekin techniques , Fisher's equation , Stability , Analysis , Numerical algorithm
[1] Allaire, P. E. (1985) Basics of the Finite Element Method, Wm. C. Brown Publishers.
[2] Fisher, R.A. (1937) “The Wave of Advance of Advantageous Genes”, Annals of Eugenics 7, pp. 355–369
[3] Fory’s, U. and A. Marciniak–Czochra, (2003) “Logistic Equations in
Tumour Growth Modelling”, Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 3, pp. 317–325.
[4] Gourley, S.A. (2000) “Travelling Front Solutions of a Nonlocal Fisher Equation”, J. Math. Biol. 41, pp. 272–284.
[5] Logan, J. D. (1987) Applied Mathematics, John Wiley and Sons.
[6] Manaa, Saad A. and B.M. Ibrahim, (2004) “Stability Analysis for A Fully Developed Laminar Fluid Flow in A Rectangular Bend with Secondary Flow”, Raf. Jour. Sci., Vol. 15, No.1, Math & Stati., Special Issue, pp. 146-152.
[7] Ortega–Cejas, V.; J. Fort, and V. Mendez, (2004) “The Role of The Delay Time in The Modeling of Biological Range Expansions”, J. Ecology, 85 (1), pp. 258–264.
[8] Pesin, Y. and A. Yurchenko, (2004) “Some Physical Models of The
Reaction–Diffusion Equation and Coupled Map Lattices”, Russian Math. Surveys, Vol. 8, No. 3,pp.177-218.
[9] Puri, S. and Wiese, K. J. (2003) “Perturbative Linearization of Reaction–Diffusion Equations”, J. Phys., A36, pp.2043-2054.
[10] Sasaki, T. (2004) “The Effect of Local Prevention in an Sis Model With Diffusion”, Discrete and Continuous Dynamical Systems Series B, Vol. 4, No. 3 , PP. 739–746
[11] Smith, G. D. (1965) Numerical Solution of Partial Differential Equations, Oxford University Press
