An efficient algorithm for parameterized magnetohydrodynamic flow ensembles simulation

Mohebujjaman, Muhammad; Wang, Hongwei; Rebholz, Leo G.; Mahbub, Md. Abdullah Al

doi:10.1016/j.camwa.2022.02.014

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…The linearity of the schemes provides the uniqueness of the solution via their the stability theorem. Because of the finite dimensional and linearity features, the uniqueness implies existence of the solution, therefore the solution to the Algorithm 1 and 2 exist uniquely [14,23].…”

Section: Stability Analysismentioning

confidence: 99%

“…The harvesting and/or stocking parameter can be a useful controlling tool in the population dynamics with limited natural resources. As a future research, we will propose, analyze and test an efficient decoupled algorithm for this N -species competition model following the works in [22,23] so that at each time-step each species solver shares a common system matrix which will further save computer memory and assembling time of system matrix.…”

Section: Conclusion and Futurementioning

confidence: 99%

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Decoupled algorithms for non-linearly coupled reaction-diffusion competition model with harvesting and Stocking

Mohebujjaman¹,

Clarisa²,

Kamrujjaman³

et al. 2022

Preprint

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We propose, analyze and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled reaction-diffusion N -species competition model with harvesting or stocking effort. The time-stepping algorithms are first and second order accurate in time and optimally accurate in space. Stability and optimal convergence theorems of the decoupled schemes are proven rigorously. We verify the predicted convergence rates of our analysis and efficacy of the algorithms using numerical experiments and synthetic data for analytical test problems. We also study the effect of harvesting or stocking and diffusion parameters on the evolution of species population density numerically, and observe the co-existence scenario subject to optimal harvesting or stocking.

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Section: Stability Analysismentioning

confidence: 99%

Section: Conclusion and Futurementioning

confidence: 99%