No abstract

In this paper, numerical solution of the advection-diffusion equation is obtained by using extended cubic B-spline functions. For space discretization, the extended cubic B-spline Galerkin method is used to integrate the advection-diffusion equation and for time discretization, the Crank-Nicolson method is employed to obtain the fully integrated advection-diffusion equation. The maximum error norm has been used to show the accuracy of the method. Robustness of the suggested method is shown by studying some classical test problems and comparing the results with some earlier ones.

In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation (RLW) is integrated fully by using an exponential B-spline Galerkin method in space together with Crank-Nicolson method in time. Three numerical examples related to propagation of single solitary wave, interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers' equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers' equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on some well-known problems for the Burgers' equation.

In this paper, an application of the quartic trigonometric B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method based on the quartic trigonometric B-spline function in space discretization together with second and fourth order schemes in time discretization. The accuracy of the proposed methods are demonstrated by test problems and numerical results are compared with the exact solution and some previous results.