Polynomial scaling functions for numerical solution of generalized Kuramoto–Sivashinsky equation

Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

“…where t is the mesh size in the time direction, 0 ≤ θ ≤ 1 and y j+1 is used to denote y(x, t j + t). The nonlinear term (yy x ) j+1 is treated as [33] (…”

“…Gomes et al [32] used linear feedback controls and techniques to stabilize the non-uniform unstable steady states of the generalized KS equation. The authors in [33] used polynomial scaling functions for solving the generalized KS equation. Akgul and Bonyah [34] proposed a reproducing kernel Hilbert space method for the solving generalized KS equation.…”

A new two-level implicit scheme of order two in time and four in space based on half-step spline in compression approximations for unsteady 1D quasi-linear biharmonic equations

“…Most recently, Mohanty and Kaur [18] developed a Numerov type compact variable mesh method for the solution of KS equation. A polynomial scaling function technique was used by Rashidinia and Jokar [19] for solving the GKS equation. Danumjaya and Pani [20] constructed a numerical scheme based on an orthogonal cubic spline collocation method for the solution of EFK equation.…”

Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation

“…J. Yang et al in [12] used the sine-cosine method and dynamic bifurcation method to solve the more generalized GKSE and its related equations to Equation (1). In [13], J. Rashidinia et al solved Equation (1) by Chebyshev wavelets. O. Acan et al applied the reduced differential transform method to solve Equation (1) by taking β = 0 in [14].…”

“…Ravi et al in [33], A. R. Seadawy et al in [34] and M. Nur Alam et al in [35]; the Jacobi elliptic function method by S. Liu et al in [36]; the F-expansion method by A. Ebaid et al in [37]; and the extended G G method by E. M. E. Zayed and S. Al-Joudi et al in [38]. The GKSE Equation (1) does not have the solution for general α and β; however, for the different values of α and β, the solution exists for (1), which can be found in [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In this work, we apply the modified Kudryashov method (MKM) to solve the GKSE in which we compute the constants α and β by the MKM.…”