Lead-Acid Battery Model Under Discharge With a Fast Splitting Method

Harwood, R. Corban; Manoranjan, V. S.; Edwards, Dean B.

doi:10.1109/tec.2011.2162093

Cited by 25 publications

(22 citation statements)

References 18 publications

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“…Operator-splitting techniques very effectively handle the nonlinearity and complexity of reaction-diffusion equations. Therefore, these techniques are used frequently by several researchers for the solution of nonlinear differential equations [23,[25][26][27][28][29][30][31][32][33]. The SEIQV epidemic model with diffusion is split in two ways.…”

Section: Methodsmentioning

confidence: 99%

“…In finite difference operator splitting techniques, the step involving the reaction term is unconditionally stable because it is solved exactly [25,26]. On the other hand, the step involving the diffusion term has different stability in different techniques.…”

Section: Stability and Accuracy Of Splitting Schemesmentioning

confidence: 99%

“…while the implicit procedure has unconditionally stability [25,26]. The accuracy of both schemes is O(τ ) and O(h 2 ) for all the methods under study.…”

Section: Stability and Accuracy Of Splitting Schemesmentioning

confidence: 99%

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Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

et al. 2020

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In this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.

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Section: Methodsmentioning

confidence: 99%

Section: Stability and Accuracy Of Splitting Schemesmentioning

confidence: 99%

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Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

et al. 2020

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“…In similar fashion, we can equivalently express the systems (38)- (42) and (39)- (43) with their respective homogeneous Neumann boundary conditions as…”

Section: Numerical Propertiesmentioning

confidence: 99%

“…To close this section, we must point out that the stability and the consistency of the splitting schemes is based on the use of the split solutions [33,42]. Recall that the first time-step in operator splitting techniques consists in handling the discretization of the reaction terms.…”

mentioning

confidence: 99%

Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

2019

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In this work, we numerically investigate a three-dimensional nonlinear reaction-diffusion susceptible-infected-recovered hepatitis B epidemic model. To that end, the stability and bifurcation analyses of the mathematical model are rigorously discussed using the Routh-Hurwitz condition. Numerically, an efficient structure-preserving nonstandard finite-difference time-splitting method is proposed to approximate the solutions of the hepatitis B model. The dynamical consistency of the splitting method is verified mathematically and graphically. Moreover, we perform a mathematical study of the stability of the proposed scheme. The properties of consistency, stability and convergence of our technique are thoroughly analyzed in this work. Some comparisons are provided against existing standard techniques in order to validate the efficacy of our scheme. Our computational results show a superior performance of the present approach when compared against existing methods available in the literature.

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Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Harwood

2017

Foundations for Undergraduate Research in Mathematics

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A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but this can be misleading if the method is not developed and operated carefully due to numerical oscillations, instabilities, and other artifacts of the programmed solution. This chapter provides a friendly introduction to error analysis of numerical methods for nonlinear partial differential equations along with modern approaches to visually demonstrate analytical results with confidence. These techniques are illustrated through several detailed examples with a relevant governing equation, and lead to open questions suggested for undergraduate-accessible research. Suggested prerequisites. differential equations, linear algebra, some programming experience arXiv:1802.08785v2 [math.HO]

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Lead-Acid Battery Model Under Discharge With a Fast Splitting Method

Cited by 25 publications

References 18 publications

Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

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