Open AccessA Numerical Method for Solving the Mobile/Immobile Diffusion Equation with Non-Local Conditions
Author(s) -
I. I. Gorial
Publication year - 2021
Publication title -
mathematical modelling and engineering problems/mathematical modelling of engineering problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.26
H-Index - 11
eISSN - 2369-0747
pISSN - 2369-0739
DOI - 10.18280/mmep.080408
Subject(s) - convergence (economics) , variable (mathematics) , mathematics , boundary value problem , diffusion equation , fractional calculus , initial value problem , work (physics) , exact solutions in general relativity , mathematical optimization , mathematical analysis , mechanical engineering , economy , economic growth , engineering , economics , service (business)
The purpose of this work is to use a new numerical technique for solving the two-sided multi-dimensional variable order fractional mobile/immobile diffusion equation with non-local conditions (TSMDVOF-MIDENLCs) model using the variable time fractional derivative of Caputo, as well as an initial boundary value problem of modified treatment. We used the fractional variational iteration method (FVIM) to mix initial and boundary conditions, resulting in for each iteration, a new initial solution. Convergence, sufficient conditions (SC) for system convergence, and error estimation are discussed. Some examples are given to illustrate the applicability of the novel suggested method, demonstrating that the numerical solution matches the exact solution and that the error is zero. Furthermore, this algorithm is easy and inexpensive to implement, and it demonstrates efficiency and accuracy.