A quadratic B-spline Galerkin approach for solving a coupled KdV equation

In this paper, a quadratic B-spline Galerkin finite element approach is applied to one-dimensional coupled KdV equation in order to obtain its numerical solutions. The performance of the method is examined on three test problems. Computed results are compared with the exact results and also other numerical results given in the literature. A Fourier stability analysis of the approach is also done

An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers' equation

In the present paper, two effective numerical schemes depending on a second-order Strang splitting technique are presented to obtain approximate solutions of the one-dimensional Burgers' equation utilizing the collocation technique and approximating directly the solution by multiquadric-radial basis function (MQ-RBF) method. To show the performance of both schemes, we have considered two examples of Burgers' equation. The obtained numerical results are compared with the available exact values and also those of other publishedmethods. Moreover, the computed L-2 and L-infinity error norms have been given. It is found that the presented schemes produce better results as compared to those obtained almost all the schemes present in the literature

A Fresh Look To Exact Solutions of Some Coupled Equations

This manuscript is going to seek travelling wave solutions of some coupled partial differential equations with an expansion method known as Sine- Gordon expansion method. Primarily, we are going to employ a wave transformation to partial differential equation to reduce the equations into ordinary differential equations. Then, the solution form of the handled equations is going to be constructed as polynomial of hyperbolic trig or trig functions. Finally, with the aid of symbolic computation, new exact solutions of the partial differentials equations will have been found