Results 171 to 180 of about 238 (195)
Axioms, 2023 This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from fractional calculus.
Azzh Saad Alshehry +2 more
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The Second Alternative to the Optimal Auxiliary Functions Method
2021In this Chapter, we present an alternative to the OAFM. For the nonlinear differential equation.
Vasile Marinca +2 more
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The First Alternative of the Optimal Auxiliary Functions Method
2021In this chapter, we will actually solve the Eq. (2.13) from which the first approximation \(u_{1} (x,C_{i} )\) can be determined.
Vasile Marinca +2 more
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Extension of optimal auxiliary function method to nonlinear Sine Gordon differential equations
Partial Differential Equations in Applied MathematicsIn this paper, the new semi-analytical method called optimal auxiliary function method has been extended for finding the approximate solution of the non-linear Sine Gordon and Burger equations. The parameters of the auxiliary function’s optimum values control convergence, and they were determined using the well-known collocation approach.
Rashid Nawaz, Nick Fewster-Young
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International Journal of Emerging Multidisciplinaries: Mathematics, 2022
This paper extends the application of Optimal Auxiliary Function Method (OAFM) to the system of integral equations. The system of Volterra integral equations of second kind are taken as test examples. The results obtained by proposed method are compared with different methods i.e., Biorthogonal systems in a Banach space Fixed point, the implicit ...
Laiq Zada, Falak Naz, Rashid Nawaz
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This paper extends the application of Optimal Auxiliary Function Method (OAFM) to the system of integral equations. The system of Volterra integral equations of second kind are taken as test examples. The results obtained by proposed method are compared with different methods i.e., Biorthogonal systems in a Banach space Fixed point, the implicit ...
Laiq Zada, Falak Naz, Rashid Nawaz
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A new global optimization technique by auxiliary function method in a directional search
Optimization Letters, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
ŞAHİNER, Ahmet, Ibrahem, Shehab A.
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2021
In this Chapter, we will present some particular cases in which we can determine exact solutions to nonlinear dynamical systems. More precisely, for nonlinear dynamical systems given by the nonlinear differential equation.
Vasile Marinca +2 more
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In this Chapter, we will present some particular cases in which we can determine exact solutions to nonlinear dynamical systems. More precisely, for nonlinear dynamical systems given by the nonlinear differential equation.
Vasile Marinca +2 more
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2020
The optimal auxiliary functions method is implemented in this paper to derive an analytical approximate solution for the problem of nonlinear vibrations of doubly clamped nanobeam incorporating the Casimir force. A closed form solution is obtained. This model accounts for the inherent nonlinearity of the Casimir force and the geometric nonlinearity of ...
Vasile Marinca, Nicolae Herisanu
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The optimal auxiliary functions method is implemented in this paper to derive an analytical approximate solution for the problem of nonlinear vibrations of doubly clamped nanobeam incorporating the Casimir force. A closed form solution is obtained. This model accounts for the inherent nonlinearity of the Casimir force and the geometric nonlinearity of ...
Vasile Marinca, Nicolae Herisanu
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Physica Scripta
Abstract In this work, we solve the fractional-order Fornberg-Whitham (FW) problem in the context of the Caputo operator by using the Optimal Auxiliary Function Method. Tables and figures showing full numerical findings indicate the correctness and efficacy of this strategy.
Naveed Iqbal +3 more
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Abstract In this work, we solve the fractional-order Fornberg-Whitham (FW) problem in the context of the Caputo operator by using the Optimal Auxiliary Function Method. Tables and figures showing full numerical findings indicate the correctness and efficacy of this strategy.
Naveed Iqbal +3 more
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2018
Rotating electrical machines are widely used in engineering and industry applications due to their reliability. The machines under study are subjected to a parametric excitation caused by an inertial thrust and a forcing excitation caused by an unbalanced force of the rotor while the entire system is being supported by nonlinear bearings with nonlinear
Nicolae Herisanu, Vasile Marinca
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Rotating electrical machines are widely used in engineering and industry applications due to their reliability. The machines under study are subjected to a parametric excitation caused by an inertial thrust and a forcing excitation caused by an unbalanced force of the rotor while the entire system is being supported by nonlinear bearings with nonlinear
Nicolae Herisanu, Vasile Marinca
openaire +1 more source