Browsing by Author "Qureshi, S."

Now showing 1 - 2 of 2

Citation - Scopus: 4
Symmetry Analysis and Some New Exact Solutions of the Newell-Whitehead and Zeldovich Equations
(Cankaya University, 2019) Yusuf, A.; Baleanu, Dumitru; Ghanbari, B.; Qureshi, S.; Inc, M.; Baleanu, D.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The present study offers an overview of Newel-Whitehead-Segel (NWS) and Zeldovich equations (ZEE) equations by Lie symmetry analysis and generalizes rational function methods of exponential function. Some novel complex and real-valued exact solutions for the equations under consideration are presented. Using a new conservation theorem, we construct conservation laws for the ZEE equation. The physical expression for some of the solutions is presented to shed more light on the mechanism of the solutions. © 2019, Cankaya University. All rights reserved.
Citation - Scopus: 1
Transformation of Halley’s Computationalmethod Into Its Optimal Nonlinear Variant
(L and H Scientific Publishing, LLC, 2024) Baleanu, D.; Alshomrani, A.S.; Qureshi, S.; Soomro, A.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The approach of solving nonlinear models with numerical techniques is on the rise owing to the omnipresence of the models in several scientific fields. This paper developed an optimal variant of Halley’s method without memory of order five for solving nonlinear equations w(x) = 0. The technique is one-step with five function evaluations required in each iteration and has an efficiency index of 1.38. The idea of basins of attraction to study the suggested technique’s influence on the initial estimation is considered that reveals stable nature. This is also supported by various numerical examples that show how the proposed approach performs compared to other existing techniques. For examples considered, such as Vander Waals’ equation and continuously stirred tank reactors, the proposed method without memory arrives at approximations to the roots with fewer iterations and better accuracy. Convergence analysis is also discussed to prove the fifth-order accuracy and complex dynamics is discussed via polynomiographs. © 2024, L&H Scientific Publishing, LLC. All rights reserved.