Numerical solution to a one-dimensional nonlinear problem of heat wave propagation in a rigid thermal conducting slab

Sweilam, N. H.; Ghaleb, A. F.; Abou-Dina, M. S.; Hasan, M. M. Abou; AL–Mekhlafi, S.M.; Rawy, E. K.

doi:10.1007/s12648-020-01952-8

Cited by 3 publications

(1 citation statement)

References 40 publications

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“…This method is simple to implement [24], and it can be used to improve the discretizations of some terms in differential equations so that depending on the denominator function and the specific discretization, it is more accurate and stable than the standard method ( [23]). This technique is used in physics, chemistry, and engineering( [15], [14], [16], ( [17],…”

Section: Introductionmentioning

confidence: 99%

Nonstandard finite difference treatment of a differential game problem

Alabdullah¹,

Hasan²,

Siedyb³

2023

Preprint

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This paper presents and analyses some Mean Field Games (MFGs) models that depict interactions between two groups where the number of participants tends to +infinity.Solutions to differential game problems, systems of partial differential equations. MFGtheory equations have been developed to approximate the static and evolutionary versions of such models. We present numerical methods and simulations. To solve the problem in the resulting system of equations, we propose nonstandard finite difference schemes for the optimal planning problem, which has an optimal control formulation. We also conduct numerical tests. Mathematics Subject Classification: 65M06, 33F05.

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Section: Introductionmentioning

confidence: 99%

Nonstandard finite difference treatment of a differential game problem

Alabdullah¹,

Hasan²,

Siedyb³

2023

Preprint

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Dynamical analysis of a nonlinear fractional cervical cancer epidemic model with the nonstandard finite difference method

Butt,

Ahmad Saqib,

Alshomrani

et al. 2024

Ain Shams Engineering Journal

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Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip

Abou Hasan,

Ahmed,

Ghaleb

et al. 2024

Fluids

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An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed lower plate, and the motion is triggered by the motion of the upper plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion.

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Numerical solution to a one-dimensional nonlinear problem of heat wave propagation in a rigid thermal conducting slab

Cited by 3 publications

References 40 publications

Nonstandard finite difference treatment of a differential game problem

Nonstandard finite difference treatment of a differential game problem

Dynamical analysis of a nonlinear fractional cervical cancer epidemic model with the nonstandard finite difference method

Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip

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