Novel Cubic Trigonometric B-Spline Approach Based on the Hermite Formula for Solving the Convection-Diffusion Equation

Abstract

This paper introduces a cubic trigonometric B-spline method (CuTBM) based on the Hermite formula for numerically handling the convection-diffusion equation (CDE). The method utilizes a merger of the CuTBM and the Hermite formula for the approximation of a space derivative, while the time derivative is discretized using a finite difference scheme. This combination has greatly enhanced the accuracy of the scheme. A stability analysis of the scheme is also presented to confirm that the errors do not magnify. The main advantage of the scheme is that the approximate solution is obtained as a smooth piecewise continuous function empowering us to approximate a solution at any location in the domain of interest with high accuracy. Numerical tests are performed, and the outcomes are compared with the ones presented previously to show the superiority of the presented scheme.

Numerical Solutions of Advection-Diffusion Equation via Quartic B-Spline Least Squares Method

“…and using transformation (10) for derivative in 𝜁𝜁 coordinates, the first and second derivatives becomes…”

“…The fourth order single step methods for time integration and cubic B-spline Galerkin method for space integration is used to solve ADE in the work [9]. The cubic trigonometric B-spline for space discretization and finite difference scheme for time discretization is established to discretize the ADE fully [10]. ADE is also handled by means of the least squares method.…”

Recent Advances in Multiphase Flows in Engineering

“…Yousaf et al [6] presented a novel method known as the cubic trigonometric B-spline technique based on the Hermite formula. ey used this method to solve the convection-diffusion equation.…”