An Attractive Analytic-Numeric Approach for the Solutions of Uncertain Riccati Differential Equations using Residual Power Series

Authors

Mohammad Alshammari, Department of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor, Bangi 43600, MalaysiaFollow
Mohammad Al-Smadi, Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanFollow
Saleh Alshammari, Department of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor, Bangi 43600, MalaysiaFollow
Omar Abu Arqub, Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, JordanFollow
Ishak Hashim, Department of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor, Bangi 43600, MalaysiaFollow
Mohd Almie Alias, Department of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor, Bangi 43600, MalaysiaFollow

Author Country (or Countries)

Malaysia

Abstract

In this paper, the analytic-approximate solution for a class of quadratic Riccati differential equation under uncertainty is obtained using a modified residual power series (RPS) expansion algorithm. The proposed method is a well-known efficient precise algorithm to address numerous issues in physics and engineering. The RPS is a systematic tool based on the use of the Taylor approach and residual error concept by minimizing error functions to determine the values of the coefficients of the PS according to given initial data of symmetric triangular fuzzy numbers. To interpret the solutions of fuzzy quadratic Riccati equations, the strongly-generalized differentiability sense is implemented. This algorithm provides an approximate series of solutions within a radius suitable for the desired domain. Numerical applications are introduced to clarify the compatibility and reliability of the RPS algorithm. The gained results confirm that the suggested simulated is highly reliable, simple and can be implemented to other classes of nonlinear uncertain natural problems.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140202

Recommended Citation

Alshammari, Mohammad; Al-Smadi, Mohammad; Alshammari, Saleh; Abu Arqub, Omar; Hashim, Ishak; and Almie Alias, Mohd (2020) "An Attractive Analytic-Numeric Approach for the Solutions of Uncertain Riccati Differential Equations using Residual Power Series," Applied Mathematics & Information Sciences: Vol. 14: Iss. 2, Article 2.
DOI: http://dx.doi.org/10.18576/amis/140202
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss2/2