A study of mimetic and finite difference methods for the static diffusion equation

Jones, Giselle Sosa; Arteaga, Joaquin; J., Jiménez, Oswaldo

doi:10.1016/j.camwa.2018.05.004

Cited by 2 publications

(1 citation statement)

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“…On the other hand, the moving least squares approach is implemented to reconstruct continuous functions from a set of unorganized point samples [22][23][24][25][26]. As another discretization scheme, the finite difference method converts linear/nonlinear differential equations into a system of linear/non-linear algebraic equations [27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of the Volterra differential equations via a combination of evolutionary algorithms with moving least squares and finite difference methods

Mahmoodabadi

2021

J. eng.

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In this paper, the Volterra differential equations governing on the predator-prey dynamics is numerically solved through the combination of evolutionary algorithms with Moving Least Squares as well as the Finite Difference Method. Among the numerous evolutionary algorithms, the Genetic Algorithms and Particle Swarm Optimization, as two powerful and effective approaches, are selected. The penalty method is chosen to impose the initial conditions on the objective function, while the Moving Least Squares is implemented to interpolate the derivatives in the differential equations. In order to illustrate the effectiveness of the Moving Least Squares, the results are compared with those obtained via the Finite Difference Method based evolutionary algorithms. Moreover, the results are associated with those of a numerical method and an analytical scheme to evaluate the obtained populations of the prey and the predator. These comparisons clearly illustrate the reliability and efficiency of the proposed methodology to solve nonlinear differential equations. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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