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Fisher's equation, which describes the logistic growth-diffusion process and occurs in many biological and chemical processes, has been studied numerically by the wavelet Galerkin method. Wavelets are functions which can provide local finer details. The solution of Fisher's equation has a compact support property and therefore Daubechies' compactly supported wavelet basis has been used in this study. The results obtained by the present method are highly encouraging and can be computed for a large value of the linear growth rate.

In this paper we have studied the numerical stationary solution of viscous Burgers' equation with Neumann boundary conditions by applying wavelet Galerkin method. Burns et al. [J. Burns, A. Balogh, D.S. Gilliam, and V. I. Shubov, Numerical stationary solutions for a viscous Burgers'equation, J. Maths. Sys. Est. Contl. 8 (1998), pp. 1-16] have reported that for moderately small viscosity and for certain initial conditions, numerical solution approaches non-constant shock-type stationary solution though only possible actual stationary solution is a constant. We found that the wavelet Galerkin method precisely captures the correct steady-state solution. The solutions obtained were impressive and verify theoretical results.

In this paper, we concentrate our study to derive appropriate duality theorems for two types of second-order dual models of a nondifferentiable minimax fractional programming problem involving second-order α-univex functions. Examples to show the existence of α-univex functions have also been illustrated. Several known results including many recent works are obtained as special cases. MSC: 49J35; 90C32; 49N15