Numerical study of Fisher's equation by wavelet Galerkin method

R. C. Mittal, Sumit Kumar
2006 International Journal of Computer Mathematics  
In this paper, we study the numerical solutions of Fisher's equation and to a nonlinear diffusion equation of the Fisher type by differential quadrature method. Fisher's equation combines diffusion with logistic nonlinearity. The equation occurs in logistic population growth models, neurophysiology and nuclear reactions. Therefore, numerical study of these types of equations is very important. In this work, differential quadrature method is discussed and applied on four examples of representing
more » ... different types of Fisher's equations. Numerical results show the accuracy and utility of the differential quadrature method in solving such problems. equation were not present till 1974s in the literature. First numerical solutions of Fisher's equation were presented by Gazdag and Canosa [10] with a pseudo-spectral approach. After that, a number of researchers have solved Fisher's equation numerically. Parekh and Puri [19] and Twizell et al. [27] have presented the implicit and explicit finite differences algorithms to discuss the numerical study of Fisher's equation. Hagstrom and Keller [11] have developed asymptotic boundary conditions by using centered finite difference algorithm. Tang and Weber [26] proposed a Galerkin finite element method and Rizwan-Uddin [24] compared the nodal integral method and non standard finite-difference schemes. Carey and Shen [9] used a least-squares finite element method and Al-Khaled [3] proposed sinc collocation method. Mickens [16] proposed a best
doi:10.1080/00207160600717758 fatcat:km5ypvdtivbvhnoeqwkumnb3tm