Browsing by Author "Torkzadeh, Leila"

Now showing 1 - 8 of 8

Citation - WoS: 13
Citation - Scopus: 14
Investigation on Ginzburg-Landau Equation Via a Tested Approach To Benchmark Stochastic Davis-Skodje System
(Elsevier, 2021) Ranjbar, Hassan; Baleanu, Dumitru; Torkzadeh, Leila; Nouri, Kazem
We propose new numerical methods with adding a modified ordinary differential equation solver to the Milstein methods for solution of stiff stochastic systems. We study a general form of stochastic differential equations so that the Ginzburg-Landau equation and the Davis-Skodje model can be considered as special states of them. The efficiency of the method is experimented, in terms of the convergence rate and accuracy of approximate solution, employing some numerical examples, including stochastic Ginzburg-Landau equation and a paradigm of chemical reaction systems. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 6
Citation - Scopus: 6
An Iterative Algorithm for Robust Simulation of the Sylvester Matrix Differential Equations
(Springer, 2020) Beik, Samaneh Panjeh Ali; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are applied to convert the main equation to the matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained equations. Also, the error analysis of the propounded method is presented, which reveals the spectral rate of convergence. To illustrate the effectiveness of the proposed framework, several numerical examples are given.
Citation - WoS: 7
Citation - Scopus: 7
Numerical Method for Pricing Discretely Monitored Double Barrier Option by Orthogonal Projection Method
(Amer inst Mathematical Sciences-aims, 2021) Fahimi, Milad; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
In this paper, we consider discretely monitored double barrier option based on the Black-Scholes partial differential equation. In this scenario, the option price can be computed recursively upon the heat equation solution. Thus we propose a numerical solution by projection method. We implement this method by considering the Chebyshev polynomials of the second kind. Finally, numerical examples are carried out to show accuracy of the presented method and demonstrate acceptable accordance of our method with other benchmark methods.
Simulating systems of Itô SDEs with split-step (α, β)-Milstein scheme
(2023) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (α, β)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters α, β. Finally, numerical examples illustrate the effectiveness of the theoretical results.
Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme
(2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.
Citation - WoS: 2
Citation - Scopus: 2
Simulating Systems of Ito? Sdes With Split-Step (?, ?)-Milstein Scheme
(Amer inst Mathematical Sciences-aims, 2022) Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem; Ranjbar, Hassan
In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.
Citation - WoS: 107
Citation - Scopus: 120
Stability Analysis and System Properties of Nipah Virus Transmission: a Fractional Calculus Case Study
(Pergamon-elsevier Science Ltd, 2023) Shekari, Parisa; Torkzadeh, Leila; Ranjbar, Hassan; Jajarmi, Amin; Nouri, Kazem; Baleanu, Dumitru
In this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh-Hurwitz criterion and LaSalle's invariability principle. For the implementation of this epidemic model, we also use the Adams-Bashforth-Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.
Citation - WoS: 5
Citation - Scopus: 5
Stochastic Epidemic Model of Covid-19 Via the Reservoir-People Transmission Network
(Tech Science Press, 2022) Fahimi, Milad; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
The novel Coronavirus COVID-19 emerged in Wuhan, China in December 2019. COVID-19 has rapidly spread among human populations and other mammals. The outbreak of COVID-19 has become a global challenge. Mathematical models of epidemiological systems enable studying and predicting the potential spread of disease. Modeling and predicting the evolution of COVID-19 epidemics in near real-time is a scientific challenge, this requires a deep understanding of the dynamics of pandemics and the possibility that the diffusion process can be completely random. In this paper, we develop and analyze a model to simulate the Coronavirus transmission dynamics based on Reservoir-People transmission network. When faced with a potential outbreak, decision-makers need to be able to trust mathematical models for their decision-making processes. One of the most considerable characteristics of COVID-19 is its different behaviors in various countries and regions, or even in different individuals, which can be a sign of uncertain and accidental behavior in the disease outbreak. This trait reflects the existence of the capacity of transmitting perturbations across its domains. We construct a stochastic environment because of parameters random essence and introduce a stochastic version of the Reservoir-People model. Then we prove the uniqueness and existence of the solution on the stochastic model. Moreover, the equilibria of the system are considered. Also, we establish the extinction of the disease under some suitable conditions. Finally, some numerical simulation and comparison are carried out to validate the theoretical results and the possibility of comparability of the stochastic model with the deterministic model.