Derivative-orthogonal wavelets for discretizing constrained optimal control problems

Ashpazzadeh, Elmira; Han, Bin; Lakestani, Mehrdad; Razzaghi, Mohsen

doi:10.1080/00207721.2020.1739356

Cited by 3 publications

(2 citation statements)

References 39 publications

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“…Wavelets and their generalizations appear in a variety of advanced applications in filter banks analysis, in image processing and image recognition, transmission and storage [26,28,30,27,29] . This is largely due to the fact that wavelets have the right structure to capture the sparsity in "physical" images, perfect mathematical properties such as its multi-scale structure, sparsity, smoothness, compactly supported, and high vanishing moments.…”

Section: Introductionmentioning

confidence: 99%

Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling

Mohammad

Trounev

2020

Chaos, Solitons & Fractals

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Riesz wavelets in L 2 (R ) have been proven as a useful tool in the context of both pure and numerical analysis in many applications, due to their well prevailing and recognized theory and its natural properties such as sparsity and stability which lead to a well-conditioned scheme. In this paper, an effective and accurate technique based on Riesz wavelets is presented for solving weakly singular type of fractional order integro-differential equations with applications to solve system of fractional order model that describe the dynamics of uninfected, infected and free virus carried out by cytotoxic T lymphocytes (CTL).The Riesz wavelet in this work is constructed via the smoothed pseudo-splines refinable functions. The advantage of using such wavelets, in the context of fractional and integro-differential equations, lies on the simple structure of the reduced systems and in the powerfulness of obtaining approximated solutions for such equations that have weakly singular kernels. The proposed method shows a good performance and high accuracy orders.

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Section: Introductionmentioning

confidence: 99%

Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling

Mohammad

Trounev

2020

Chaos, Solitons & Fractals

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“…In the literature, there are plenty of contributions on the use of wavelets and their generalizations to model and solve several problems of differential and integral equations of different types and applications in pure mathematics, engineering and physics; see, for example [ 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. In this paper, we use framelets with three generators generated via set of B-splines in order to solve fractional Volterra integral equations (FVIEs).…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations

Mohammad

Trounev

Cattani

2020

Entropy

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This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet, is a generalization of an orthonormal basis. A lot of applications are modeled by non-negative functions; taking this into account in this paper, we consider framelet systems generated using some refinable non-negative functions, namely, B-splines. The FVIEs we considered were reduced to a set of linear system of equations and were solved numerically based on a collocation discretization technique. We present many important examples of FVIEs for which accurate and efficient numerical solutions have been accomplished and the numerical results converge very rapidly to the exact ones.

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A robust pseudospectral method for numerical solution of nonlinear optimal control problems

Mehrpouya

Peng

2020

International Journal of Computer Mathematics

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Derivative-orthogonal wavelets for discretizing constrained optimal control problems

Cited by 3 publications

References 39 publications

Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling

Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling

An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations

A robust pseudospectral method for numerical solution of nonlinear optimal control problems

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