Solutions of fuzzy advection-diffusion and heat equations by natural adomian decomposition method

Noor Jamal; Muhammad Sarwar; Parveen Agarwal; Nabil Mlaiki; Ahmad Aloqaily

doi:10.1038/s41598-023-45207-y

Solutions of fuzzy advection-diffusion and heat equations by natural adomian decomposition method

Sci Rep. 2023 Oct 30;13(1):18565. doi: 10.1038/s41598-023-45207-y.

Authors

Noor Jamal¹, Muhammad Sarwar², Parveen Agarwal^{3

4}, Nabil Mlaiki⁵, Ahmad Aloqaily⁵

Affiliations

¹ Department of Mathematics, University of Malakand, Dir Lower, Pakistan.
² Department of Mathematics, University of Malakand, Dir Lower, Pakistan. sarwarswati@gmail.com.
³ Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE.
⁴ Department of Mathematics, Anand International College of Engineering Near Kanota, Agra Road, Jaipur, Rajasthan, 303012, India.
⁵ Department of Mathematics and General Sciences, Price Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia.

Abstract

In this article, we present an algorithm for computing analytical solutions of linear fuzzy advection-diffusion equations and one-dimensional fuzzy heat equations involving an external source. The fuzzy problems can be solved by using the natural transform and Adomian decomposition method. The results obtained through the natural Adomian decomposition method are calculated in a series form that converges rapidly to the exact solution. To enhance the practicality of our work, we provide examples to illustrate our findings.