A New Robust Iterative Scheme Applied in Solving a Fractional Diffusion Model for Oxygen Delivery via a Capillary of Tissues

Godwin Amechi Okeke (), Akanimo Victor Udo, Nadiyah Hussain Alharthi and Rubayyi T. Alqahtani
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Godwin Amechi Okeke: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria
Akanimo Victor Udo: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria
Nadiyah Hussain Alharthi: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh P.O. Box 90950, Saudi Arabia
Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh P.O. Box 90950, Saudi Arabia

Mathematics, 2024, vol. 12, issue 9, 1-30

Abstract: In this paper, we constructed a new and robust fixed point iterative scheme called the UO iterative scheme for the approximation of a contraction mapping. The scheme converges strongly to the fixed point of a contraction mapping. A rate of convergence result is shown with an example, and our scheme, when compared, converges faster than some existing iterative schemes in the literature. Furthermore, the stability and data dependence results are shown. Our new scheme is applied in the approximation of the solution to the oxygen diffusion model. Finally, our results are applied in the approximation of the solution to the boundary value problems using Green’s functions with an example.

Keywords: UO iterative scheme; boundary value problem; strong convergence; T -stability; almost T -stability; oxygen diffusion model; Green’s function; data dependence; rate of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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