Numerical solution of two-point nonlinear boundary value problems via Legendre–Picard iteration method

Tafakkori-Bafghi, M.; Loghmani, Ghasem Barid; Heydari, Mohammad

doi:10.1016/j.matcom.2022.03.022

Cited by 8 publications

(2 citation statements)

References 55 publications

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“…The proposed method was based on a combination of spectral method and variational iteration method. Tafakkori-Bafghi et al [26] introduced an effective numerical method for solving two-point nonlinear boundary value problems. The proposed iterative scheme, called the Legendre-Picard iteration method was based on the Picard iteration technique, shifted Legendre polynomials and Legendre-Gauss quadrature formula.…”

Section: Introductionmentioning

confidence: 99%

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Fadugba,

Ibrahim,

Adeyeye

et al. 2023

J. Math. Computer Sci.

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There are several nonlinear physical models emanated from science and technology that have always remained a challenge for numerical analysts and applied mathematicians. Various one-step numerical methods were developed to deal with these models, however, it requires the developed method to have consistency, stability, zero stability and convergence characteristics to handle the non-linearity in the model. This paper proposes a new sixth order inverse polynomial method (SOIPM) with a relative measure of stability for the solution of non-linear physical models with different flavors. Firstly, the properties of SOIPM are analyzed and investigated. Moreover, three illustrative non-linear physical models have been solved to measure the accuracy, computational performance, suitability and effectiveness of SOIPM. Furthermore, the results generated via SOIPM are compared with the existing method of the celebrated Runge-Kutta of order four (RK4) in the context of the exact value (EV). Finally, the absolute errors (ABEs) and final absolute errors (FABEs) incurred by SOIPM are computed and compared with that of RK4.

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Section: Introductionmentioning

confidence: 99%

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Fadugba,

Ibrahim,

Adeyeye

et al. 2023

J. Math. Computer Sci.

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“…The research on BVPs is one of the important areas in applied and computational mathematics because it plays an essential role in modeling real-life problems in astrophysics, heat transfer, fluid mechanics and dynamics and physical and chemical phenomena such as electromagnetic radiation reactions, chemical reactor theory, isothermal packed-bed reactor and numerous other real-world differential problems, which can be modeled by Equations ( 1)-(4). For more details about the application of BVPs for modeling real-life differential problems, see [27][28][29][30]. Motivated by the different applications of the BVPs in real-world modeling problems in applied sciences and engineering mentioned above and with the aims of improving the accuracy of some existing methods for solving Equations ( 1)- (4), in this research paper, a new two-point third-derivative hybrid block method (TDHBM) is proposed to provide a better numerical solution to BVP in Equations ( 1)-(4).…”

Section: Introduction and Description Of The Problemmentioning

confidence: 99%

An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs

Rufai

2022

Mathematics

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A new one-step hybrid block method with two-point third derivatives is developed to solve the second-order boundary value problems (BVPs). The mathematical derivation of the proposed method is based on the interpolation and collocation methods. The theoretical properties of the proposed method, such as consistency and convergence, are well analysed. Some BVPs with different boundary conditions are solved to demonstrate the efficiency and feasibility of the suggested method. The numerical results of the proposed method are much closer to the exact solutions and more competitive than other numerical methods in the available literature.

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Piecewise Jacobi–Gauss spectral collocation simulations for a multi-particle model involving processing delay

Zhou,

Wang,

et al. 2024

Comp. Appl. Math.

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Numerical solution of two-point nonlinear boundary value problems via Legendre–Picard iteration method

Cited by 8 publications

References 55 publications

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs

Piecewise Jacobi–Gauss spectral collocation simulations for a multi-particle model involving processing delay

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