Compact finite difference method to numerically solving a stochastic fractional advection-diffusion equation

Sweilam, N. H.; El-Sakout, D. M.; Muttardi, M. M.

doi:10.1186/s13662-020-02641-w

Cited by 4 publications

(2 citation statements)

References 44 publications

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“…From (3.5) and (3.7), the conditions, necessary and sufficient for OPC are We construct a theorem similar to that presented in [28][29][30][31][32], [44][45][46][47].…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Mahdy¹,

Mohamed²,

Amiri³

et al. 2022

Intelligent Automation &Amp; Soft Computing

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In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through drawing before and after control. Fractional request differential equations (FDEs) are usually used to display frameworks that have memory and exist in a few thermoelasticity models and organic standards. FDEs show the realistic biphasic decline of infection of diseases but at a slower rate. FDEs are more suitable than integer order ones in modeling complex systems, such as biological systems.

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“…From (3.5) and (3.7), the conditions, necessary and sufficient for OPC are We construct a theorem similar to that presented in [28][29][30][31][32], [44][45][46][47].…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Mahdy¹,

Mohamed²,

Amiri³

et al. 2022

Intelligent Automation &Amp; Soft Computing

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“…In [13], explicit and implicit finite difference methods were proposed to obtain the solution of general SPDEs. In [14], a stochastic compact finite difference scheme was suggested for solving a stochastic fractional advection-diffusion equation. In [15], high-resolution finite volume methods were used to solve SPDEs.…”

Section: Introductionmentioning

confidence: 99%

A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

Băleanu¹,

Namjoo²,

Mohebbian³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution.

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Fourth-Order Numerical Solutions for a Fuzzy Time-Fractional Convection–Diffusion Equation under Caputo Generalized Hukuhara Derivative

et al. 2022

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The fuzzy fractional differential equation explains more complex real-world phenomena than the fractional differential equation does. Therefore, numerous techniques have been timely derived to solve various fractional time-dependent models. In this paper, we develop two compact finite difference schemes and employ the resulting schemes to obtain a certain solution for the fuzzy time-fractional convection–diffusion equation. Then, by making use of the Caputo fractional derivative, we provide new fuzzy analysis relying on the concept of fuzzy numbers. Further, we approximate the time-fractional derivative by using a fuzzy Caputo generalized Hukuhara derivative under the double-parametric form of fuzzy numbers. Furthermore, we introduce new computational techniques, based on fuzzy double-parametric form, to shift the given problem from one fuzzy domain to another crisp domain. Moreover, we discuss some stability and error analysis for the proposed techniques by using the Fourier method. Over and above, we derive several numerical experiments to illustrate reliability and feasibility of our proposed approach. It was found that the fuzzy fourth-order compact implicit scheme produces slightly better results than the fourth-order compact FTCS scheme. Furthermore, the proposed methods were found to be feasible, appropriate, and accurate, as demonstrated by a comparison of analytical and numerical solutions at various fuzzy values.

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Compact finite difference method to numerically solving a stochastic fractional advection-diffusion equation

Cited by 4 publications

References 44 publications

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Optimal Control and Spectral Collocation Method for Solving Smoking Models

A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

Fourth-Order Numerical Solutions for a Fuzzy Time-Fractional Convection–Diffusion Equation under Caputo Generalized Hukuhara Derivative

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