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Analytical Approximate Solution of Chemical Kinetics Problems [PDF]
Computational Algorithms and Numerical Dimensions, 2022 In this article, the chemical kinetics problem is presented. The Differential Transformation Method (DTM) is presented to find an approximate analytical solution to the chemical kinetics problems.
Hatıra Günerhan
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Solving fractional partial differential equations via a new scheme
AIMS Mathematics, 2023 In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative.
Ahmad Qazza, Rania Saadeh, Emad Salah
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A three-free-parameter class of power series based iterative method for approximation of nonlinear equations solution [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 In this manuscript, for approximation of solutions to equations that are nonlinear, a new class of two-point iterative structure that is based on a weight function involving two converging power series, is developed.
O. Ogbereyivwe, O. Izevbizua
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Mathematics, 2022 The paper studies a degenerate nonlinear parabolic equation containing a convective term and a source (reaction) term. It considers the construction of approximate solutions to this equation with a specified law of diffusion wave motion, the existence of
Alexander Kazakov, Lev Spevak
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Axioms, 2023 The Laplace residual power series method was introduced as an effective technique for finding exact and approximate series solutions to various kinds of differential equations.
Haneen Khresat +4 more
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Semi-Analytical Methods in the Problem of Deformation of a Fluid Strip
Mathematics, 2023 A problem from a class of unsteady plane potential flows with a free boundary is considered. The entire boundary occupied by the liquid is free, and a zero pressure is maintained. There are neither external nor capillary forces.
Evgenii Karabut, Elena Zhuravleva
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Effective algorithms for solving functional equations with superposition on the example of the Feigenbaum equation [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамика, 2023 Purpose. New algorithms were consider for functional equations solving using the Feigenbaum equation as an example. This equation is of great interest in the theory of deterministic chaos and is a good illustrative example in the class of functional ...
Polunovskii, Andrey Andreevich
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A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate
International Journal of Applied Mechanics and Engineering, 2020 The intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique.
Pradeep Mohan, R. Ramesh Kumar
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Numerical approach for approximating the Caputo fractional-order derivative operator
AIMS Mathematics, 2021 This work aims to propose a new simple robust power series formula with its truncation error to approximate the Caputo fractional-order operator $ D_{a}^{\alpha}y(t) $ of order $ m-1 < \alpha < m $, where $ m\in\mathbb{N} $.
Ramzi B. Albadarneh +3 more
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Fibonacci Series from Power Series [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived.
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