Applications of Homotopy Perturbation Transform Method for Solving Newell-Whitehead-Segel Equation

Abstract

In the present work, we apply an analytical method known as Homotopy Perturbation Transform Method, is used for solving Newell-Whitehead-Segel Equation. Five tests are examined to validate the accuracy of this algorithm. Numerical results show that the proposed method is a more reliable, efficient and convenient one for solving different cases of Newell-Whitehead-Segel equation.

Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics

“…Eq. ( 34) becomes Newell-Whitehead equation [25], having initial condition: and the exact solution is…”

Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations

“…Consider the Equation ( 1) with the values of constants as n = 4, α = 1 and β = −1, which gives the NW equation of the following form the [63] ∂v…”

“…Utilizing the value of h in v 4 (x, t, h) in the domain (x, t) [0, 1] × [0, 1], the comparison of exact and MVIA-II solutions can be seen in Figure 5 for different values of t, while to prove the effectiveness of the suggested technique for various values of t, x and absolute errors in Table 5 along with the results of homotopy perturbation transform technique given in [63]. One can ensure that the results of MVIA-II are more accurate and can be obtained in a very short time.…”