Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation
Demonstratio Mathematica, 2023 The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders.
El-Sayed Adel Abd Elaziz
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An efficient variable stepsize rational method for stiff, singular and singularly perturbed problems
Alexandria Engineering Journal, 2022 In this article, a new iterative method of the rational type having fifth-order of accuracy is proposed to solve initial value problems. The method is self-starting, stable, consistent, and convergent, whereas local truncation error analysis has also ...
Sania Qureshi +5 more
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Analysis and new simulations of fractional Noyes-Field model using Mittag-Leffler kernel
Scientific African, 2022 In this manuscript, the fractional-in-time NoyesField model for Belousov-Zhabotinsky reaction transport is considered with a novel numerical technique, which was used to approximate the Atangana-Baleanu (ABC) operator which models the subdiffusion ...
Berat Karaagac +2 more
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A new adaptive nonlinear numerical method for singular and stiff differential problems
Alexandria Engineering Journal, 2023 In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life.
Sania Qureshi +6 more
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Computational dynamics of predator-prey model with the power-law kernel
Results in Physics, 2021 Evolution system which contains fractional derivatives can give rise to useful mathematical model for describing some important real-life or physical scenarios.
Kolade M. Owolabi
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The solution of Cahn-Allen equation based on Bernoulli sub-equation method
Results in Physics, 2019 In this article, we present an analytical method for finding the solutions of the Cahn-Allen equation (CAE) based on the Bernoulli sub-equation method (BSEM). We find an infinite number of solutions which are divided into eight families.
Muhammed I. Syam
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Orthogonal-Based Second Order Hybrid Initial Value Problem Solver
Fountain Journal of Natural and Applied Sciences (FUJNAS), 2016 This work focuses on development of an initial value problem solver by employing a new class of orthogonal polynomial, the basis function. We present the recursive formula of the class of polynomials constructed and adopt collocation technique to ...
E. O. Adeyefa +3 more
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A novel study for solving systems of nonlinear fractional integral equations
Applied Mathematics in Science and Engineering, 2023 In this study, we explore the solution of a nonlinear system of fractional integro-differential equations based on the operational matrix method.
Sondos M. Syam +4 more
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Pioneering Numerical Techniques for Solving Differential Equations - A Comprehensive overview [PDF]
ITM Web of ConferencesThe field of numerical analysis studies the application of mathematics to solve problems of practical importance. When solving differential equations derived from real-world scenarios, numerical techniques play a crucial role, particularly when a closed ...
Ch Swapna +2 more
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A reliable method for first order delay equations based on the implicit hybrid method
Alexandria Engineering Journal, 2020 In this paper, a reliable approach based on the implicit hybrid method is presented to solve first order delay problems. The main difficulty in this approach is that, some points are not grid points.
Muhammed I. Syam, Mohammed Al-Refai
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