The study titled “A novel method to investigate nonlinear advection-diffusion processes” led by ITU  Department of Mathematics member Prof. Dr. Murat Sari was published in Journal of Computational and Applied Mathematics.

The study introduces a new method called the reversed fixed point iteration method (RFPIM) to solve viscous and inviscid Burgers equations, which are nonlinear partial differential equations (PDEs) representing advection and diffusion phenomena. The RFPIM is effective in capturing the natural behavior of the problem even in challenging situations such as advection dominance and allows for the use of relatively large time steps, reducing the storage burden and CPU time. The method has potential for solving inverse problems and inverse optimal control problems.

https://www.sciencedirect.com/science/article/pii/S0377042723000018