International Journal of Mathematical, Engineering and Management Sciences Vol. 7, No. 5, 717-729, 2022 https://doi.org/10.33889/IJMEMS.2022.7.5.047 717 | https://www.ijmems.in Solution of Fisher Kolmogorov Petrovsky Equation Driven via Haar Scale-3 Wavelet Collocation Method Ratesh Kumar Department of Mathematics, Lovely Professional University, Punjab-144411, India. E-mail: rateshqadian@gmail.com Sonia Arora Department of Mathematics, Lovely Professional University, Punjab-144411, India. Corresponding author: soniadelhite@gmail.com (Received on February 08, 2022; Accepted on August 08, 2022) Abstract The design of the proposed study is to examine the presentation of a novel numerical techniques based on Scale-3 Haar wavelets for a kind of reaction-diffusion system i.e., Fisher KPP (Kolmogorov Petrovsky Piskunove) Equation. Haar scale-3 wavelets are employed to space and time derivatives approximation involved in the system. The collocation approach is applied with space and time variables discretization to construct an implicit and explicit numerical scheme for the reaction-diffusion system. We have used various numerical problems containing non-linearity and different source term to inquest the exactness, efficiency and authenticity of the proposed numerical strategy. In addition, the obtained results are graphically displayed and systematized. Even with a small number of collocation Points, we attain accuracy using the presented technique. Keywords- Fisher KPP; Haar Scale-3; Collocation points; Reaction-diffusion system. 1. Introduction Fisher (1937) and Kolmogorov et al. (1937) independently scrutinized the Fisher-Kolmogorov-Petrovsky Piskunove equation in 1937, which is now known as the Fisher equation. This equation can be used in a variety of scientific and technical domains (Franak, 1969; Arora and Kumar, 2020; Dhwan et al., 2014; Canosa, 2015). Many studies have been conducted in order to find a relevant explanation and stereotype of this equation (Man et al., 2019; Branco et al., 2007; Dhwan et al., 2013, Dhwan et al., 2021). We looked at one stereotype of this equation, which is known as the component reaction-diffusion equation collectively. Traveling wave fronts are present in many reaction-diffusion equations and play a vital role in the understanding the concepts of physical, biological, and physical events (Wawa and Gorguis, 2004; Kaur and Wazwaz, 2021). Reaction-diffusion systems are mathematical models that describe how the congregation of one or more materials scattered in space changes as a result of two processes: general chemical reactions, which involved transformation of substances into one another, and diffusion, in which substances open up over a surface in space. Reaction diffusion systems (Franak-Kameneetiskii, 1969) are commonly used in chemistry. On the other hand, the system can be used to express non-chemical dynamical processes. For a single substance's concentration in a single spatial dimension, the most basic reaction-diffusion equation. The equation reflects pure diffusion if the response term is removed, and it becomes a parabolic partial equation in one spatial dimension if the thermal diffusivity term substitutes the diffusion term D. The KPP Fisher equation with isentropic is used to explain native agitation in advective environments (Gu et al., 2015).