An application of cubic B-Spline finite element method for the Burgers` equation

It is difficult to achieve exact solution of non-linear PDE, directly. Sometimes, it is possible to convert non-linear PDE into equivalent linear PDE by applying a convenient transformation. Hence, Burgers? equation replaces with heat equation by means of the Hope-Cole transformation. In this study, Burgers? equation was converted to a set of non-linear ODE by keeping non-linear structure of Burgers? equation. In this case, solutions for each of the non-linear ODE were obtained by the help of the cubic B-spline finite element method. Model problems were considered to verify the efficiency of this method. Agreement of the solutions was shown with graphics and tables.

Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method

In this paper, we are going to obtain numerical solutions of the improved Boussinesq equation with the aid of Galerkin quadratic B-spline finite element method. To test the accuracy and efficiency of the current method, four test problems have been used. These are solitary wave movement, interaction of two solitary waves, wave break-up and blow-up of solutions. Their results have been compared with those available in the literature for different values of space and time steps. Also, the error norms L2 and L1 have been computed and presented in comparison.