A numerical solution of Burgers’ equation by modified Adomian method

An efficient scheme for numerical solution of Burgers’ equation using quintic Hermite interpolating polynomials

“…A variety of numerical methods have been developed to solve the Burgers' equation, such as finite difference scheme [12,14], finite element method [2], quadratic B-spline [13,16], cubic B-spline [5,9], automatic differentiation [6], and modified Adomain method [1]. In the present study, numerical solution of Burgers' equation has been shown by applying the quintic Hermite collocation method directly, without transforming the non-linear form into the linear form using Hopf-Cole transformation.…”

A New Efficient Method for Solving Two-Dimensional Burgers' Equation

“…Nonlinear phenomena play a crucial role in applied mathematics and physics. The importance of obtaining the exact or approximate solutions of PDEs in physics and mathematics is still a hot topic as regards seeking new methods for obtaining new exact or approximate solutions [2][3][4][5]. For that purpose, different methods have been put forward for seeking various exact solutions of multifarious physical models described using nonlinear PDEs.…”

New soliton solutions for Kaup-Boussinesq system

“…Also, the explicit formulas may provide physical information and help us to understand the mechanism of related physical models. Recently, there have been a multitude of methods presented for solving Nonlinear partial differential equations (NPDEs), for instance, the Adomian decomposition method [1],the homotopy perturbation method [2],the variational iteration method [3,4] , the He's variational approach [5], the F −expansion method [6], three-wave method [7], extended homoclinic test approach [8,9], the ( G G )−expansion method [6] and the exp-function method [10].…”