The approximate solutions of nonlinear Boussinesq equation

A Note on the Application of the Double Sumudu–Generalized Laplace Decomposition Method and 1+1- and 2+1-Dimensional Time-Fractional Boussinesq Equations

“…The Boussinesq equation appears in different fields, such as a one-dimensional nonlinear lattice [2], shallow-water waves [3,4], and the propagation of longitudinal deformation waves in an elastic rod [5]. Throughout the past three decades, several methods have been developed and applied to solve Boussinesq equations, for example, the modified decomposition method (see [6][7][8]), homotopy analysis and homotopy perturbation methods [9][10][11], and the Laplace Adomian decomposition method [12][13][14]. A fractional Boussinesq equation is acquired by assuming power-law changes in flux in a control volume and applying a fractional Taylor series [15].…”

A new quintic B-spline approximation for numerical treatment of Boussinesq equation

“…Siddiqi and Arshad [20] proposed quintic B-spline (QnBS) collocation approach for approximate solution of classical non-linear BE. The authors in [18] employed homotopy analysis method (HAM) to explore the analytical solution of BE with variable coefficients. Zakaria et al [25] used quintic trigonometric B-spline collocation method (QnTBSM) to study the numerical solution of BE.…”

On Some Initial and Initial Boundary Value Problems for Linear and Nonlinear Boussinesq Models

“…During the last three decades, many methods have been developed and used to solve these equations, such as homotopy analysis and homotopy perturbation methods (Francisco and Fernández [6], Gupta and Saha [7] and Dianhen et al [8]), the analytic method [9], the modified decomposition method (Wazwaz [10], Fang et al [11] and Basem and Attili [12]) the Laplace Adomian Decomposition Method (Hardik et al [13], Zhang et al [14], Liang et al [15]) the transformed rational function method (Wang [16], Engui [17]) the integral transform method (Charles et al [18]) the energy integral method (Joseph [19], Mesloub [20]) the inverse scattering method (Peter et al [21]) and other different numerical methods were used to investigate problems dealing with Boussinesq equations, see for example, Jang [22], Iskandar and Jain [23], Bratsos [24], Dehghan and Salehi [25], Boussinesq [26], and Onorato et al [27]. For the bifurcation of solutions and possible applications of Boussinesq equations, we may refer to References [28,29].…”