Computational modelling
A method based on the SCT to solve the inverse problem for heat equation

Samaneh Akbarpour; Abdollah Shidfar; Hashem Saberi Najafi

Articles in Press, Accepted Manuscript, Available Online from 02 December 2021

  In this article, a mathematical model of the inverse problem is considered. Basedon this model a formulation of inverse problem for heat equation is proposed.Shifted Chebyshev Tau (SCT) method is suggested to solve the inverse problem. The aim of this determined effort is to identify unknown function ...  Read More

Computational modelling
Numerical approximation for the fractional advection-diffusion equation using a high order difference scheme

Zahra Mahboob Dana; Hashem Saberi Najafi; Amir Hossein Refahi Sheikhani

Volume 8, Issue 1 , March 2021, , Pages 90-103

  In this paper, a one-dimensional fractional advection-diffusion equation is considered. First, we propose a numerical approximation of the Riemann-Liouville fractional derivative which is fourth-order accurate, then a numerical method for the fractional advection-diffusion equation using a high order ...  Read More

Mathematical modelling
A fully implicit non-standard finite difference scheme for one dimensional Burgers' equation

Abdolrahman Yaghoobi; Hashem Saberi Najafi

Volume 7, Issue 3 , September 2020, , Pages 301-312

  In this paper we have studied a numerical approximation to the solution of the nonlinear Burgers' equation. The presented scheme is obtained by using the Non-Standard Finite Difference Method (NSFD). The use of NSFD method and its approximations play an important role for the formation of stable numerical ...  Read More