Redefined fourth order uniform hyperbolic polynomial B-splines based collocation method for solving advection-diffusion equation

Abstract

In the present paper, uniform hyperbolic polynomial (UHP) B-spline based collocation method is proposed for solving advection-diffusion equation (ADE) numerically. The Von-Neumann's criterion is used to perform stability analysis. It reveals that the proposed scheme is unconditionally stable. The proposed method is implemented on various examples and numerical outcomes which are reported in table. The numerical outcomes are compared with the other methods available in standard literature. The rate of convergence is also calculated numerically which is found to be closed to 2. The numerical investigation reveals that the developed scheme is efficient, accurate and easy to implement. The proposed method is also applied to solve two-dimensional and three-dimensional ADE to demonstrate the efficiency of proposed scheme.