Nonclassical pseudospectral method for the solution of brachistochrone problem

Alipanah, Amjad; Razzaghi, Mohsen; Dehghan, Mehdi

doi:10.1016/j.chaos.2006.04.071

Cited by 14 publications

(6 citation statements)

References 19 publications

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“…The nonclassical pseudospectral methods [11,12,20] expand the function f ∈ L 2 [a, b]by using weighted interpolations of degree N of the form [11,12] (…”

Section: Nonclassical Pseudospctral Discretization Methodsmentioning

confidence: 99%

Nonclassical Pseudospectral Method for a Class of Singular Boundary Value Problems Arising in Physiology

Alipanah¹

2012

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In this paper, nonclassical pseudospectral method is presented for solution of a classof nonlinear singular boundary value problems arising in physiology. Properties of non-classical pseudospectral method are presented. These properties are utilizeto reduce the computation of singular boundary value problems to system of equations. Numerical method is tested for its efficiency by considering two examples from physiology

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“…The nonclassical pseudospectral methods [11,12,20] expand the function f ∈ L 2 [a, b]by using weighted interpolations of degree N of the form [11,12] (…”

Section: Nonclassical Pseudospctral Discretization Methodsmentioning

confidence: 99%

Nonclassical Pseudospectral Method for a Class of Singular Boundary Value Problems Arising in Physiology

Alipanah¹

2012

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“…The proposed Algorithms 2 and 3 are implemented in MATLAB , where for solving the optimal control subproblems to , the optimality conditions for linear cases and the trapezoid direct transcription for nonlinear cases are used. Of course, there are more sophisticated direct methods, such as pseudospectral methods and other methods, which can be used for solving the optimal control subproblems.…”

Section: Numerical Illustrationmentioning

confidence: 99%

Extragradient methods for differential variational inequality problems and linear complementarity systems

Fatemi

Shamsi

Bozorgnia³

2017

Math Methods in App Sciences

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In this paper, 2 extragradient methods for solving differential variational inequality (DVI) problems are presented, and the convergence conditions are derived. It is shown that the presented extragradient methods have weaker convergence conditions in comparison with the basic fixed-point algorithm for solving DVIs. Then the linear complementarity systems, as an important and practical special case of DVIs, are considered, and the convergence conditions of the presented extragradient methods are adapted for them. In addition, an upper bound for the Lipschitz constant of linear complementarity systems is introduced. This upper bound can be used for adjusting the parameters of the extragradient methods, to accelerate the convergence speed.Finally, 4 illustrative examples are considered to support the theoretical results. KEYWORDS differential variational inequality, extragradient method, fixed point problem, linear complementarity system, optimal control problem, variational inequalities Math Meth Appl Sci. 2017;40:7201-7217.wileyonlinelibrary.com/journal/mma

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“…[10] designed a method for solving Euler's equations with nonlinear source term. Alipanah et al [11] solved the classic brachistochrone problem using nonclassical pseudospectral method. Generalized fractional-order Chebyshev wavelet method is used to solve distributed-order fractional optimal control problems [12].…”

Section: Introductionmentioning

confidence: 99%

Bernoulli wavelet least square support vector regression: Robust numerical method for systems of fractional differential equations

Rahimkhani

Ordokhani

Sabermahani

2022

Preprint

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In this study, a new hybrid method is developed to solve a system of linear or nonlinear fractional differential equations using Bernoulli wavelets (Bws) and the least square support vector regression(LS-SVR). For this purpose, we present Bw operator of Riemann-Liouville fractional integration for Bw and use it in our scheme. In the proposed technique, we approximate the unknown functions via Bws, then with the help of Bw operator of fractional integration and LS-SVR, we reduce the problem to an algebraic system. In this way, we simplify the computation of the considered system. The error analysis is proposed. Finally, we demonstrate the applicability of the present scheme by solving several numerical examples.

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Nonclassical pseudospectral method for the solution of brachistochrone problem

Cited by 14 publications

References 19 publications

Nonclassical Pseudospectral Method for a Class of Singular Boundary Value Problems Arising in Physiology

Nonclassical Pseudospectral Method for a Class of Singular Boundary Value Problems Arising in Physiology

Extragradient methods for differential variational inequality problems and linear complementarity systems

Bernoulli wavelet least square support vector regression: Robust numerical method for systems of fractional differential equations

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