Adapted numerical modelling of the Belousov-Zhabotinsky reaction

被引：6

作者：

D'Ambrosio, Raffaele ^{[1
]}

Moccaldi, Martina ^{[2
]}

Paternoster, Beatrice ^{[2
]}

Rossi, Federico ^{[3
]}

机构：

[1] Univ Aquila, Dept Engn & Comp Sci & Math, Laquila, Italy

[2] Univ Salerno, Dept Math, Fisciano, SA, Italy

[3] Univ Salerno, Dept Chem & Biol, Fisciano, SA, Italy

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2018年 / 56卷 / 10期

关键词：

Oscillating solutions; Exponential fitting; Adapted Runge-Kutta methods; Parameter estimation; Reaction equations; Belousov-Zhabotinsky reaction; Chemical oscillators; RUNGE-KUTTA METHODS; CHEMICAL-REACTION; SYSTEMS; DYNAMICS; OSCILLATIONS; MECHANISM; FRONTS;

D O I：

10.1007/s10910-018-0922-5

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

Adapted numerical schemes for the integration of differential equations generating periodic wavefronts have reported benefits in terms of accuracy and stability. This work is focused on differential equations modelling chemical phenomena which are characterized by an oscillatory dynamics. The adaptation is carried out through the exponential fitting technique, which is specially suitable to follow the apriori known qualitative behavior of the solution. In particular, we have merged this strategy with the information coming from existing theoretical studies and especially the observation of time series. Numerical tests will be provided to show the effectiveness of this problem-oriented approach.

引用

页码：2876 / 2897

页数：22

共 40 条

[1] A NEW THEORETICAL APPROACH TO RUNGE-KUTTA METHODS
ALBRECHT, P
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (02) : 391 - 406
[2] Belousov B. P., 1959, OSCILLATING REACTION
[3] A Novel Mechanism for in Situ Nucleation of Spirals Controlled by the Interplay between Phase Fronts and Reaction-Diffusion Waves in an Oscillatory Medium
Budroni, Marcello A.
Rossi, Federico
[J]. JOURNAL OF PHYSICAL CHEMISTRY C, 2015, 119 (17) : 9411 - 9417
[4] Exponential fitting Direct Quadrature methods for Volterra integral equations
Cardone, Angelamaria
Ixaru, Liviu Gr.
Paternoster, Beatrice
[J]. NUMERICAL ALGORITHMS, 2010, 55 (04) : 467 - 480
[5] Revised exponentially fitted Runge-Kutta-Nystrom methods
D'Ambrosio, R.
Paternoster, B.
Santomauro, G.
[J]. APPLIED MATHEMATICS LETTERS, 2014, 30 : 56 - 60
[6] Exponentially fitted two-step Runge-Kutta methods: Construction and parameter selection
D'Ambrosio, R.
Esposito, E.
Paternoster, B.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (14) : 7468 - 7480
[7] Exponentially fitted two-step hybrid methods for y" = f (x, y)
D'Ambrosio, R.
Esposito, E.
Paternoster, B.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (16) : 4888 - 4897
[8] D'Ambrosio R., 2018, ART LIF EV COMP WIV
[9] On the Employ of Time Series in the Numerical Treatment of Differential Equations Modeling Oscillatory Phenomena
D'Ambrosio, Raffaele
Moccaldi, Martina
Paternoster, Beatrice
Rossi, Federico
[J]. ADVANCES IN ARTIFICIAL LIFE, EVOLUTIONARY COMPUTATION, AND SYSTEMS CHEMISTRY, WIVACE 2016, 2017, 708 : 179 - 187
[10] Adapted numerical methods for advection-reaction-diffusion problems generating periodic wavefronts
D'Ambrosio, Raffaele
Moccaldi, Martina
Paternoster, Beatrice
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (05) : 1029 - 1042

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