Modeling of Nonstationary Distributed Processes on the Basis of Multidimensional Time Series

Matveev, Mikhail; Kopytin, A.V.; Sirota, E. A.; Kopytina, Ekaterina

doi:10.1016/j.proeng.2017.09.643

Cited by 6 publications

(1 citation statement)

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“…These model's problems contain parameters that must be specified to uniquely determine the result of boundary value problems. But in practice, situations frequently arise when some of these parameters are unknown or given roughly and they need to be determined or clarified [5,6]. Applications of ecology, geophysics, and seismology have also arisen in the form of advection-reaction-diffusion or convection-reaction-diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

Investigation the Accuracy of Crank Nicolson Methods and their Modified Schemes for One-Dimensional Linear Convection-Reaction-Diffusion Equations

Koroche

2024

AJOMCOR

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In this paper, Crank-Nicolson and Their Modified scheme are applied to find the solution of the convection-reaction-diffusion equation. First, the given solution domain is discretized. Then, using Taylor series expansion, we obtain the difference scheme of the model problem. By rearranging this scheme, we gain proposed techniques. To verify the validity of the proposed techniques, two model illustrations are considered. The stability and convergent analysis of the present scheme is worked by supporting the theoretical and numerical error bound. The accuracy of the present scheme has been shown in the sense of average absolute error, root means square error, and maximum absolute error norms. Then, the accuracy of the present techniques is compared with the accuracy obtained by another method in the literature. The physical behavior of the present results also has been shown in terms of graphs. As we can seen from the results in tables and physical behavior of solution, the present scheme approximates the exact solution veritably well. These scheme is improve the approximation exact solution of convection-reaction-diffusion equation. Hence, the present solution of convection-reaction-diffusion equation is accurate than pre-existing solution.

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Section: Introductionmentioning

confidence: 99%