Numerical Simulation of the Dispersion of Pollutant in a Canal

Gbenro, S. O.; Nchejane, J. N.

doi:10.9734/arjom/2022/v18i430371

Cited by 3 publications

(4 citation statements)

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“…There have been various investigations on the numerical solutions of variants of the nonlinear Schrödinger equation based on either the finite difference [10,9,23,24]] and the finite element, the spectral methods. Most of these studies have been devoted to the NLS equation solutions that have a special solution with the form of a pulse, that is, solitons, keeping their shapes and velocities after an interaction.…”

Section: Original Research Articlementioning

confidence: 99%

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Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Nchejane

Gbenro²

2022

JAMCS

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The nonlinear Schrödinger equation in one-dimensional coordinate is investigated numerically by employing explicit and implicit finite difference methods. It is shown that the explicit method is conditionally stable, and the condition for stability, which is a function of the time step and spatial step size, or several grid points are obtained. It is also shown that the implicit scheme is unconditionally stable and results in a tridiagonal matrix at each time level as a function of the nonlinear term. The effects of dispersion and nonlinearity concerning the time and space steps are also investigated. The validity of our scheme is established by reproducing some existing results on the constant-coefficient nonlinear Schrödinger equation. The schemes are then extended to study the variable coefficient equation, which has a growing interest and applications in many areas of nonlinear science.

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Section: Original Research Articlementioning

confidence: 99%

“…To calculate the matrix we should upper estimate the function via upper estimation of all matrices using the matrix spectral norm [23]. Thus, we have , (24) Let us divide the matrix for the symmetric and antisymmetric parts. We use Schwartz and triangle inequalities to estimate mixed terms and the commutator .…”

Section: Explicit Schemementioning

confidence: 99%

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Nchejane

Gbenro²

2022

JAMCS

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“…We apply the implicit finite difference on the spatial variable and the Euler scheme for the time variable in the following sections. It has already been proved that an implicit scheme converges, and it is stable unconditionally [22,23]].…”

Section: Finite Difference Schemementioning

confidence: 99%

Numerical Simulation of the Evolution of Wound Healing in the 3D Environment

Nchejane

Gbenro²,

Thakedi

2022

JAMCS

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Numerical simulation of the wound healing behaviour by considering the coupled reaction-diffusion, transport and viscoelastic system is vital in investigating the mechanical stress field induced by cell migration. In this work, numerical simulation is viewed in three-dimensional space during a time course of wound healing. Over the years, many authors have developed two-dimensional mathematical models of wound healing, as supported by the background in the introduction below. But we know that a three-dimensional case realistically captures the tissue deformations. The two-dimensional simulation is restricted to observing the motion in two directions only. Hence, the interest is in the three-dimensional case. Therefore, to our knowledge, this is the first article to consider the numerical simulation of the coupled reaction-diffusion, transport and viscoelastic system during wound healing in a three-dimensional environment. Firstly, the two-dimensional evolution of wound healing is developed to compare our results with published data. Then the work is extended to three-dimensional wound healing, which is the main focus.

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“…Similarly, other types of differential equations such as fractional-order differential equation, Caputo fractional-order derivative, Fuzzy Volterra integral equation have been treated using diverse approach such as establishing the existence and stability of solution [4,5,6,7,8]; Laplace Adomain Decomposition method [9]; Haar Wavelets method [10]; and finite difference method [11,12,13,14] among others.…”

Section: Introductionmentioning

confidence: 99%

One-step three-parameter optimized hybrid block method for solving first order initial value problems of ordinary differential equations

E. A. Areo,

Gbenro,

Olabode

et al. 2024

J. Math. Anal. Model.

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A one-step three-parameter optimized hybrid block method and second derivative hybrid block method with optimized points were proposed to solve first-order ordinary differential equations. The techniques of interpolation and collocation were adopted for the derivation of the methods using a three-parameter approximation. The hybrid points were obtained by optimizing the local truncation error of the method. The schemes obtained were reformulated to reduce the number of occurrences of the source term. The hybrid points were used in the derivation of the second derivative hybrid block method. The discrete schemeswere produced as a by-product of the continuous scheme and used to simultaneously solve initial value problems (IVPs) in block mode. The resulting schemes are self-starting, do not require the creation of individual predictors, and are consistent, zero-stable, and convergent. The accuracy and efficiency of the methods were ascertained using several numerical test problems. The numerical results were favourably compared to some techniques from the cited literature.

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Numerical Simulation of the Dispersion of Pollutant in a Canal

Cited by 3 publications

References 0 publications

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Numerical Simulation of the Evolution of Wound Healing in the 3D Environment

One-step three-parameter optimized hybrid block method for solving first order initial value problems of ordinary differential equations

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