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

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 11، 4 (Fall) - شماره پیاپی 44، اسفند 2021   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2021.684829

نویسندگان

Hamid Reza Yazdani^{* 1}؛ Mehdi Nadjafikhah²؛ Megerdich Toomanian³

¹Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran

²School of Mathematics, Iran University of Science and Technology, Narmak, Tehran

³Department of Mathematics, Karaj Branch Islamic Azad University, Karaj

چکیده

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 coefficient
fu_tt(x,t) + u_t(x,t) = u_xx(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.

کلیدواژه‌ها

Father wavelet؛ Multiresolution analysis (MRA)؛ Invariant solution؛ Approximation subspace؛ Wavelet subspace؛ The GFKPP equation