Galerkin Method for the numerical solution of the advection-diffusion equation by using exponential B-splines

TL;DR

This paper introduces a numerical method using exponential B-splines to solve the advection-diffusion equation, demonstrating improved accuracy and efficiency through two illustrative examples and comparison with previous studies.

Contribution

The paper presents a novel application of exponential B-splines for solving the advection-diffusion equation, enhancing numerical accuracy and efficiency.

Findings

Accurate solutions for pure advection in a finite channel.

Effective Gaussian pulse distribution modeling.

Comparison shows improved performance over earlier methods.

Abstract

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples\ related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.