Applied Mathematics, Computational Mathematics, Numerical Analysis, Statistics and Probability
20
Scopus Publications
335
Scholar Citations
10
Scholar h-index
11
Scholar i10-index
Scopus Publications
Enhancing the Euler–Maruyama integrator via a balancing strategy for stochastic Volterra integral equations Hassan Ranjbar, Afshin Babaei Results in Applied Mathematics, 2025 This paper develops the balanced Euler–Maruyama integrator for stochastic Volterra integral equations. First, an upper bound for the designed integrator is rigorously established in the mean square sense. Next, the scheme is proved to give a strong convergence rate of 1/2 for general diffusion matrices. Furthermore, for a special case of diffusion matrices, we theoretically detect that the established integrator super-converges with strong order 1.0. Numerical experiments are provided to confirm the theoretical findings.
An explicit Milstein-type scheme for simulation of SDEs Hassan Ranjbar Filomat, 2025 In the present paper, we developed a new explicit Milstein-type integrator for stiff SDEs. Theoretically, we indicate that the scheme converges to the true value with a strong order of 1.0. For linear scalar SDE, the asymptotic mean square stability of our method is investigated. For all time steps, we prove that the presented integrator is asymptotically mean square stable. In addition, the A-stability and L-stability of the scheme was discussed in the mean square sense. For dimension two of the submitted scheme, the asymptotic mean square stability of two test systems has been analyzed. Numerical simulations confirm the theoretical results.
Analysis of a stochastic model for a prey–predator system with an indirect effect Leila Torkzadeh, Milad Fahimi, Hassan Ranjbar, Kazem Nouri International Journal of Computer Mathematics, 2025 In the current work, we develop and analyse a prey–predator model as a semi-Kolmogorov population model in which the predator has an indirect effect on the prey. The functional response of the model is investigated as Holling type (II). We construct a stochastic environment because of the parameter's random essence to study the influence of environmental fluctuations on this model and introduce a stochastic version of the prey–predator model. Then we present a dynamical analysis of solutions, including existence, uniqueness, positivity, stochastic boundedness, and stochastic extinction of all prey. Finally, some numerical simulations are carried out to validate our theoretical findings and confirm the efficiency and adaptation of our stochastic model.
Simulating systems of Itô SDEs with split-step (α, β)-Milstein scheme Hassan Ranjbar, Leila Torkzadeh, Dumitru Baleanu, Kazem Nouri Aims Mathematics, 2023 <abstract><p>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.</p></abstract>
Convergence and Stability of a Split-Step Exponential Scheme Based on the Milstein Methods Leila Torkzadeh, Hassan Ranjbar, Sanda Micula, Kazem Nouri Symmetry, 2022 We introduce two approaches by modifying split-step exponential schemes to study stochastic differential equations. Under the Lipschitz condition and linear-growth bounds, it is shown that our explicit schemes converge to the solution of the corresponding stochastic differential equations with the order 1.0 in the mean-square sense. The mean-square stability of our methods is investigated through some linear stochastic test systems. Additionally, asymptotic mean-square stability is analyzed for the two-dimensional system with symmetric and asymmetric coefficients and driven by two commutative noise terms. In particular, we prove that our methods are mean-square stable for any step-size. Finally, some numerical experiments are carried out to confirm the theoretical results.
Modifying the split-step θ-method with harmonic-mean term for stochastic differential equations International Journal of Numerical Analysis and Modeling, 2020
Enhancing the Euler–Maruyama integrator via a balancing strategy for stochastic Volterra integral equations H Ranjbar, A Babaei Results in Applied Mathematics 28, 100671 , 2025 2025
Split-step ϑ integrator for generalized stochastic Volterra integro-differential equations H Ranjbar Mathematics and Computers in Simulation 233, 165-186 , 2025 2025 Citations: 1
An explicit Euler scheme for generalized n-dimensional second-order differential equations with initial value conditions driven by additive Gaussian white noises H Ranjbar Journal of Computational and Applied Mathematics 454, 116179 , 2025 2025 Citations: 2
Analysis of a stochastic model for a prey–predator system with an indirect effect L Torkzadeh, M Fahimi, H Ranjbar, K Nouri International Journal of Computer Mathematics 102 (1), 60-73 , 2025 2025 Citations: 11
An explicit Milstein-type scheme for simulation of SDEs H Ranjbar Filomat 39 (8), 2501-2524 , 2025 2025
An exponential split-step double balanced Milstein scheme for SODEs with locally Lipschitz continuous coefficients H Ranjbar Journal of Applied Mathematics and Computing 70 (1), 809-837 , 2024 2024 Citations: 5
Analytical and numerical investigation of stochastic differential equations with applications using an exponential Euler–Maruyama approach. H Ranjbar, L Torkzadeh, K Nouri Computational & Applied Mathematics 42 (1) , 2023 2023 Citations: 3
Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study D Baleanu, P Shekari, L Torkzadeh, H Ranjbar, A Jajarmi, K Nouri Chaos, Solitons & Fractals 166, 112990 , 2023 2023 Citations: 146
Convergence and stability of a split-step exponential scheme based on the Milstein methods L Torkzadeh, H Ranjbar, S Micula, K Nouri Symmetry 14 (11), 2413 , 2022 2022 Citations: 5
Simulating systems of Ito? SDEs with split-step (?,?)-Milstein scheme H Ranjbar, L Torkzadeh, D Baleanu, K Nouri 2022 Citations: 2
Balanced-Euler approximation schemes for stiff systems of stochastic differential equations H Ranjbar, L Torkzadeh, K Nouri Filomat 36 (19), 6791-6804 , 2022 2022 Citations: 2
Improvement of Split‐Step Forward Milstein Schemes for SODEs Arising in Mathematical Physics H Ranjbar, K Nouri, L Torkzadeh Mathematical Problems in Engineering 2022 (1), 7498865 , 2022 2022 Citations: 2
Investigation on Ginzburg-Landau equation via a tested approach to benchmark stochastic Davis-Skodje system K Nouri, H Ranjbar, D Baleanu, L Torkzadeh Alexandria Engineering Journal 60 (6), 5521-5526 , 2021 2021 Citations: 17
Numerical Simulation and Methodology Based on Improved Split Step Method for Studying Stochastic Models L Torkzadeh, H Ranjbar Fuzzy Optimization and Modeling Journal (FOMJ) 2 (4), 1-9 , 2021 2021
Construction of New Implicit Milstein-Type Scheme for Solution of the Systems of SODEs H Ranjbar, Y Akbari, H Derikvandi Fuzzy Optimization and Modeling Journal (FOMJ) 2 (3), 36-46 , 2021 2021
The explicit approximation approach to solve stiff chemical Langevin equations K Nouri, H Ranjbar, L Torkzadeh The European Physical Journal Plus 135 (9), 758 , 2020 2020 Citations: 13
Solving the stochastic differential systems with modified split-step Euler-Maruyama method K Nouri, H Ranjbar, L Torkzadeh Communications in Nonlinear Science and Numerical Simulation 84, 105153 , 2020 2020 Citations: 13
Study on split-step Rosenbrock type method for stiff stochastic differential systems K Nouri, H Ranjbar, L Torkzadeh International Journal of Computer Mathematics 97 (4), 818-836 , 2020 2020 Citations: 14
Modifying the Split-Step -Method with Harmonic-Mean Term for Stochastic Differential Equations K Nouri, H Ranjbar, JCC López International Journal of Numerical Analysis and Modeling 17 (5), 662-678 , 2020 2020 Citations: 10
Modified stochastic theta methods by ODEs solvers for stochastic differential equations K Nouri, H Ranjbar, L Torkzadeh Communications in Nonlinear Science and Numerical Simulation 68, 336-346 , 2019 2019 Citations: 21
MOST CITED SCHOLAR PUBLICATIONS
Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study D Baleanu, P Shekari, L Torkzadeh, H Ranjbar, A Jajarmi, K Nouri Chaos, Solitons & Fractals 166, 112990 , 2023 2023 Citations: 146
Mean square convergence of the numerical solution of random differential equations K Nouri, H Ranjbar Mediterranean Journal of Mathematics 12 (3), 1123-1140 , 2015 2015 Citations: 37
Modified stochastic theta methods by ODEs solvers for stochastic differential equations K Nouri, H Ranjbar, L Torkzadeh Communications in Nonlinear Science and Numerical Simulation 68, 336-346 , 2019 2019 Citations: 21
Improved Euler–Maruyama Method for Numerical Solution of the Itô Stochastic Differential Systems by Composite Previous-Current-Step Idea K Nouri, H Ranjbar, L Torkzadeh Mediterranean Journal of Mathematics , 2018 2018 Citations: 18
Investigation on Ginzburg-Landau equation via a tested approach to benchmark stochastic Davis-Skodje system K Nouri, H Ranjbar, D Baleanu, L Torkzadeh Alexandria Engineering Journal 60 (6), 5521-5526 , 2021 2021 Citations: 17
Study on split-step Rosenbrock type method for stiff stochastic differential systems K Nouri, H Ranjbar, L Torkzadeh International Journal of Computer Mathematics 97 (4), 818-836 , 2020 2020 Citations: 14
The explicit approximation approach to solve stiff chemical Langevin equations K Nouri, H Ranjbar, L Torkzadeh The European Physical Journal Plus 135 (9), 758 , 2020 2020 Citations: 13
Solving the stochastic differential systems with modified split-step Euler-Maruyama method K Nouri, H Ranjbar, L Torkzadeh Communications in Nonlinear Science and Numerical Simulation 84, 105153 , 2020 2020 Citations: 13
Two High Order Iterative Methods for Roots of Nonlinear Equations K Nouri, H Ranjbar, L Torkzadeh Punjab University Journal of Mathematics 51 (3), 47-59 , 2019 2019 Citations: 13
Analysis of a stochastic model for a prey–predator system with an indirect effect L Torkzadeh, M Fahimi, H Ranjbar, K Nouri International Journal of Computer Mathematics 102 (1), 60-73 , 2025 2025 Citations: 11
Modifying the Split-Step -Method with Harmonic-Mean Term for Stochastic Differential Equations K Nouri, H Ranjbar, JCC López International Journal of Numerical Analysis and Modeling 17 (5), 662-678 , 2020 2020 Citations: 10
An exponential split-step double balanced Milstein scheme for SODEs with locally Lipschitz continuous coefficients H Ranjbar Journal of Applied Mathematics and Computing 70 (1), 809-837 , 2024 2024 Citations: 5
Convergence and stability of a split-step exponential scheme based on the Milstein methods L Torkzadeh, H Ranjbar, S Micula, K Nouri Symmetry 14 (11), 2413 , 2022 2022 Citations: 5
Analytical and numerical investigation of stochastic differential equations with applications using an exponential Euler–Maruyama approach. H Ranjbar, L Torkzadeh, K Nouri Computational & Applied Mathematics 42 (1) , 2023 2023 Citations: 3
An explicit Euler scheme for generalized n-dimensional second-order differential equations with initial value conditions driven by additive Gaussian white noises H Ranjbar Journal of Computational and Applied Mathematics 454, 116179 , 2025 2025 Citations: 2
Simulating systems of Ito? SDEs with split-step (?,?)-Milstein scheme H Ranjbar, L Torkzadeh, D Baleanu, K Nouri 2022 Citations: 2
Balanced-Euler approximation schemes for stiff systems of stochastic differential equations H Ranjbar, L Torkzadeh, K Nouri Filomat 36 (19), 6791-6804 , 2022 2022 Citations: 2
Improvement of Split‐Step Forward Milstein Schemes for SODEs Arising in Mathematical Physics H Ranjbar, K Nouri, L Torkzadeh Mathematical Problems in Engineering 2022 (1), 7498865 , 2022 2022 Citations: 2
Split-step ϑ integrator for generalized stochastic Volterra integro-differential equations H Ranjbar Mathematics and Computers in Simulation 233, 165-186 , 2025 2025 Citations: 1
Enhancing the Euler–Maruyama integrator via a balancing strategy for stochastic Volterra integral equations H Ranjbar, A Babaei Results in Applied Mathematics 28, 100671 , 2025 2025
