The study entitled “A new approach for the coupled advection-diffusion processes including source effects” led by ITU  Department of Mathematics member Prof. Dr. Murat Sarı  was published in Applied Numerical Mathematics.

This paper proposes a method to analyze nonlinear physical phenomena without losing their natural properties and reducing computational difficulties. The method, called the implicit backward differentiation formula-spline (BDFS) method, is used to capture the behavior of nature governed by nonlinear coupled Burgers equations with source functions. Unlike traditional approaches, the BDFS method does not require linearization or any other transformation process. The proposed approach reduces the computational cost and the need for storage space as it does not require any matrix or tensor product. The Newton and Thomas algorithms are used to solve the nonlinear and linear parts of the resulting system at each iteration, respectively. The convergence analysis of the present method is also discussed theoretically, and several examples are presented to illustrate its effectiveness.

https://www.sciencedirect.com/science/article/pii/S0168927422002847