Aug 2026· European Journal of Mathematical Analysis· 0 citations· 19 references
Abstract
In this paper, a two-step iterative method based on conformable fractional derivatives is proposed for solving nonlinear equations. The convergence analysis confirms that the method achieves fourth-order convergence. Numerical experiments on real-world problems reveal that the method significantly reduces the number of iterations compared to classical schemes. The method is also tested on several important models, including the Van der Waals equation, blood flow dynamics, population growth laws, chemical engineering models, and Planck's radiation law, demonstrating its wide applicability. Furthermore, the basin of attraction analysis shows improved stability and efficiency, highlighting the method's potential as a reliable alternative for nonlinear problem-solving.
Numerical experiments demonstrate that the 2SBBDFO method is an effective and reliable tool for solving stiff ODEs, and achieves higher accuracy and competitive computational efficiency compared to existing block BDF methods, particularly for smaller step sizes.
Adam M. Abdulrahman, Buhari Alhassan, M. Hamisu et al.· Journal of Numerical Simulat...· 0 citations
This study considers an application of differential transform method (DTM) to solving linear
and nonlinear eleventh order two-point boundary value problems discussed in [S.S. Siddiqi, G. Akram and I.
Zulfiqar. Solution of eleventh order boundary value problems using variational iteration technique. European
Journal...
Amjad Hussain, S. Mohyud-Din, A. Yıldırım· Journal of Information and C...· 0 citations
This study introduces and analyzes a three-step sequential decoupling algorithm designed to address nonlinear, fully coupled quasi-static thermo-poroelasticity systems incorporating convective transport. The finite element method is employed for spatial discretization and the backward Euler method for temporal discreti...
Fan Chen, Changqing Lv, Chen-Guang Zhou· 0 citations
Fractional iterative techniques are pivotal for modeling complex dynamic systems with enhanced accuracy. Despite their significance, scarcity of two step fractional iterative methods presents critical research gap. To fill this void, we propose a novel class of conformable two step Newton type fractional algorithm base...
Saima Akram, F. Akram, Muhammad Ibrahim· Punjab University journal of...· 0 citations
This study develops a backward hybrid block method for solving oscillatory second-order initial value problems (IVPs), which arise frequently in engineering and the physical sciences. Existing hybrid methods often struggle with stiff-oscillatory systems, lacking the robustness needed for accurate and stable solutions....
O. Titilayo, A. Afeez, Momoh Lukuman et al.· American Journal of Applied...· 0 citations
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