Highly efficient numerical scheme for solving fuzzy system of linear and non-linear equations with application in differential equations

Autor: Mudassir Shams, Nasreen Kausar, Praveen Agarwal, Shaher Momani, Mohd Asif Shah
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Applied Mathematics in Science and Engineering, Vol 30, Iss 1, Pp 777-810 (2022)
Druh dokumentu: article
ISSN: 2769-0911
27690911
DOI: 10.1080/27690911.2022.2147165
Popis: In this research, we suggested a numerical iterative scheme for investigating the numerical solution of fuzzy linear and nonlinear systems of equations, particularly where the linear or nonlinear system co-efficient is a crisp number and the right-hand side vector is a triangular fuzzy number. Triangular fuzzy systems of linear and nonlinear equations play a critical role in a variety of engineering, scientific challenges, mathematics, chemistry, physics, artificial intelligence, biology, medical, economics, finance, statistics, machine and deep learning, computer science, robotics and smart cars, programming, in the military and engineering industries, linear and nonlinear programming problems and traffic flow problems. In biomedical engineering, fluid flow problems, and differential equations, triangular fuzzy linear and nonlinear systems of equations also play a key role in determining the level of uncertainty. Convergence analysis illustrates that the proposed numerical technique's order of convergence for solving a triangular fuzzy system of linear and nonlinear equations is three. The newly developed numerical scheme was then applied to solve several triangular fuzzy boundary value problems. In terms of convergence rate, computing time, and residual error, numerical test problems indicate that the newly developed methods are more efficient than the current methods in the literature.
Databáze: Directory of Open Access Journals
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