Nonstandard theta Milstein method for solving stochastic multi-strain tuberculosis model

Sweilam, N. H.; AL–Mekhlafi, S.M.

doi:10.1186/s42787-020-00073-9

Cited by 3 publications

(4 citation statements)

References 37 publications

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“…The function φ(∆t) has the following conditions: φ(∆t) = △t+O ((△t) 2 ) , 0 < φ(∆t) ≤ 1,. Furthermore, for t in the interval (t 1 T ]" the discretization scheme of (2.3) using the nonstandard Milstein method [20] can be written as follows:…”

Section: Numerical Approaches For Stochastic-deterministic Cancer Modelmentioning

confidence: 99%

“…Secondly, for t in the interval (t 1 T ] the discretization scheme of (2.5) using the nonstandard Milstein method ( in short NMM) [20] is as follows:…”

Section: Numerical Approaches For Stochastic-deterministic Cancer Modelmentioning

confidence: 99%

“…Additionally, throughout the time period t 2 < t ≤ T , the discretization scheme of (2.9) using the nonstandard Milstein method ( in short NMM) [20] can be written as follows:…”

Section: Numerical Approaches For Stochastic-deterministic Cancer Modelmentioning

confidence: 99%

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Numerical Simulations for Deterministic-Stochastic Chaotic Cancer Model

Alalhareth

Laksaci

Boudaoui

et al. 2023

Preprint

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Some real-world problems have complicated behaviors, so in the last twoyears, piecewise calculus has been developed to more accurately depict these issues. Thispaper will elaborate on and examine cancer tumor’s chaotic model from determinism torandomness. Several scenarios are considered. The existence and the uniqueness of thesolutions of the system are proved via Mao’s theorem. Graphics of numerical schemesand their numerical simulations. AMS (MOS) Subject Classifications: 92B05, 65P20, 26A33

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Section: Numerical Approaches For Stochastic-deterministic Cancer Modelmentioning

confidence: 99%

“…Secondly, for t in the interval (t 1 T ] the discretization scheme of (2.5) using the nonstandard Milstein method ( in short NMM) [20] is as follows:…”

Section: Numerical Approaches For Stochastic-deterministic Cancer Modelmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Simulations for Deterministic-Stochastic Chaotic Cancer Model

Alalhareth

Laksaci

Boudaoui

et al. 2023

Preprint

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“…The key features of the proposed scheme are high accuracy and low CPU time; however, it does not generalize to all types of SDEs. Note that such method does not lend itself to a mean square stability analysis, as in Sweilam and Al‐Mekhlafi, 21 for example, since it cannot be written under the form of a numerical sequence.…”

Section: Introductionmentioning

confidence: 99%

An efficient spectral method for the numerical solution to some classes of stochastic differential equations

Chauvière

Djellout

2021

Math Methods in App Sciences

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We consider a new approach for the numerical approximation to some classes of stochastic differential equations driven by white noise. The proposed method shares some features with the stochastic collocation techniques, and in particular, it takes advantage of the assumption of smoothness of the functional to be approximated, to achieve fast convergence. The solution to the stochastic differential equation (SDE) is represented by means of Lagrange polynomials. The coefficients of the polynomial basis are functions of time, and they can be computed by solving a system of deterministic ordinary differential equations. Another motivation of this work lies in the novelty of the numerical scheme that does not belong to classical techniques to solve SDEs. Numerical examples are presented to illustrate the accuracy and the efficiency of the proposed method. In particular, we observe a spectral convergence for the mean and the variance of the solution.

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New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments

et al. 2022

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A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter is presented. The boundedness, existence, and positivity of the solutions for the proposed model are discussed. Two improved numerical methods are presented in this paper. The Caputo proportional constant nonstandard modified Euler–Maruyama method is introduced to study the fractional stochastic model, and the Grünwald–Letnikov nonstandard finite difference method is presented to study the hybrid fractional order deterministic model. Comparative studies with real data from Spain and Wuhan are presented.

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Nonstandard theta Milstein method for solving stochastic multi-strain tuberculosis model

Cited by 3 publications

References 37 publications

Numerical Simulations for Deterministic-Stochastic Chaotic Cancer Model

Numerical Simulations for Deterministic-Stochastic Chaotic Cancer Model

An efficient spectral method for the numerical solution to some classes of stochastic differential equations

New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments

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