Apply New Optimized MRA & Invariant Solutions on the Generalized-FKPP Equation

Subject Areas : International Journal of Mathematical Modelling & Computations

Hamid Yazdani ¹ ( Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran )
Mehdi Nadjafikhah ² ( School of Mathematics, Iran University of Science and Technology, Narmak, Tehran )
Megerdich Toomanian ³ ( Department of Mathematics, Karaj Branch Islamic Azad University, Karaj )

Received: 2021-05-11 Accepted : 2021-09-08 Published : 2021-12-01

Keywords: Father wavelet, Multiresolution analysis (MRA), Invariant solution, Approximation subspace, Wavelet subspace, The GFKPP equation,

Abstract :

So far, the numerous methods for solving and analyzing differential equations are proposed. Meanwhile; the combined methods are beneficial; one of them is the Optimized MRA method (OMRA). This method is based on the Father wavelets (dependent on the invariant solutions obtained by the Lie symmetry method) and correspondent MRA. In this paper, we apply the OMRA on the generalized version of FKPP equation (GFKPP) with function coefficientfutt(x,t) + ut(x,t) = uxx(x,t) + u(x,t) - u2(x,t),where f is a smooth function of either x or t.We will see that by the suitable Father wavelets, this method proposes attractive approximate solutions.