Solving Newell-Whitehead-Segel Equation By using Elzaki Transform and its inverse with The Homotopy Perturbation Method

Abstract

This research is a ‌combination of the homotopy ‌perturbation method with ‌Elzaki transform method ‌and Elzaki inverse to ‌solve some nonlinear ‌partial differential ‌equations. Where the method Elzaki ‌transform is not able to ‌deal with nonlinear ‌equations and find a solution by applying ‌the homotopy perturbation ‌method to solve nonlinear ‌differential equations ‌problems. The method ‌used has proven to be an ‌effective and easy way to ‌solve the nonlinear from kind ‌Newell-Whitehead-Segel ‌partial differential ‌equations, which are ‌classified and belong to ‌the category of ‌homogeneous partial ‌differential equations of ‌the second degree‌. The Elzaki transform method and Homotopy pertubation were shown to be very potent and successful integral transform methods for solving some non-linear equations when this method was compared to other well-known methods for handling the problems under consideration.

Keywords

• newell-whitehead-segel
• elzaki transform
• elzaki inverse
• homotopy perturbation method
• linear and non-linear partial differential equations