Convergence analysis and parity conservation of a new form of a quadratic explicit spline with applications to integral equations

Ferrari, Alberto J.; Lara, Luis; Marcus, Eduardo A. Santillan

doi:10.1186/s42787-020-00091-7

Cited by 1 publication

(2 citation statements)

References 13 publications

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“…. , n. In Ferrari et al [9,11] the quadratic segmentary interpolator S(t) ∈ R m was determined such that it interpolates y(t) in t k , k = 0, . .…”

Section: Numerical Schemes Consideredmentioning

confidence: 99%

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Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

Ferrari¹,

Lara²,

Olguin³

et al. 2022

TCAM

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A fractional order mathematical model that already exists in the literature, was considered. This model was established to study the effects of medicinal treatment in people infected with the human immunodeficiency virus (HIV). The importance of this study is that the model evaluates, among other parameters, the density of healthy and HIV-infected CD4+ T cells. These data are very necessary for the subject infected by the virus given the effects that an antiretroviral treatment causes in it. The objective of this work is to consider several numerical schemes that involve fractional derivatives in order to compare their behaviors and to obtain a good approximation of the mentioned model solution. Convergence of these schemes will be studied as well as sensitivity with respect to the variation of the parameters η (drug efficacy) and α (fractional derivative order). Furthermore, through the collection of medical records of people living with HIV, it is intended to determine the optimal fractional derivative order for the model and to compare it with the classical model.

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“…. , n. In Ferrari et al [9,11] the quadratic segmentary interpolator S(t) ∈ R m was determined such that it interpolates y(t) in t k , k = 0, . .…”

Section: Numerical Schemes Consideredmentioning

confidence: 99%

“…The coefficients a k ∈ R m are written as a k = ∑ n j=0 c k, j y j , where c k, j is defined by [9,11]:…”

Section: Numerical Schemes Consideredmentioning

confidence: 99%

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

Ferrari¹,

Lara²,

Olguin³

et al. 2022

TCAM

View full text Add to dashboard Cite

show abstract

Convergence analysis and parity conservation of a new form of a quadratic explicit spline with applications to integral equations

Abstract: In this study, a new form of a quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve integral equations.

Cited by 1 publication

References 13 publications

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment

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