Abstract
In this article, we propose a method for the solution of the generalized Burger–Fisher equation. The method is developed using CAS wavelets in conjunction with quasi-linearization technique. The operational matrices for the CAS wavelets are derived and constructed. Error analysis and procedure of implementation of the method are provided. We compare the results produce by present method with some well known results and show that the present method is more accurate, efficient, and applicable.
Highlights
The Burger–Fisher equation has important applications in various fields of financial mathematics, gas dynamic, traffic flow, applied mathematics, and physics
The exact solution is given in Chen and Zhang [2]: ac a2 þ bð1 þ c2Þ
Wavelet analysis is a new development in the area of applied mathematics
Summary
The Burger–Fisher equation has important applications in various fields of financial mathematics, gas dynamic, traffic flow, applied mathematics, and physics. We show a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport [1]. 1 ac c uðx; 0Þ 1⁄4 LðxÞ :1⁄4 À tan h x; 2ð1 þ cÞ ac a2 þ bð þ c2Þ. !1 c uð0; tÞ 1⁄4 EðtÞ :1⁄4 À tan h t ; að þ cÞ c2. !1 c uðx; tÞ 1⁄4 À tan h xÀ ð2Þ where a; b; and c are non-zero parameters. We use a single function and its dilations and translations to generate a set of orthonormal basis functions to represent a function. We define wavelet (mother wavelet) by Radunovic [3]: wa;bðxÞ p1ffiffiffiffiffi jaj w xÀb a
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