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On the Stability Analysis of Rational Integrator Method for the Solution of Initial Value Problems in Ordinary Differential Equation
American Journal of Mathematical and Computer Modelling
Volume 5, Issue 4, December 2020, Pages: 102-108
Received: Sep. 27, 2020; Accepted: Oct. 15, 2020; Published: Oct. 23, 2020
Authors
Agbeboh Goddy Ujagbe, Department of Mathematics, Ambrose Alli Unuversity, Ekpoma, Nigeria
Ehiemua Michael Ebhodaghe, Department of Mathematics, Ambrose Alli Unuversity, Ekpoma, Nigeria
Loko Perelah, Department of Mathematics, Bayelsa State College of Education, Sagbama, Nigeria
Article Tools Abstract PDF (465KB)
Abstract
In all numerical methods, it is necessary to ascertain the validity of any particular scheme. And this is possible to determine, by verifying the nature of the stability of that scheme. So the general stability function definition is given, from where an investigation is carried out on a class of rational integrator of order 15, to establish the region of absolute stability of the scheme, by constructing the Jordan curve. In the process of expanding the rational function, binomial theorem as well as the idea of combination process were introduced to ease the computation by using Maple-18 package. The simplification of the general rational integrator formula, is constructed from two processes namely through complex function, and then through polar analysis, The Jordan curve is constructed with the help of MATLAB package. Furthermore, it was discovered that the region of instability is on the positive side of the complex plane, while the region of absolute stability is outside the Jordan curve. Finally, it is further established that the encroachment point, τ, lie within the interval ± 140.6. And the encroachment point is visible from the corresponding values of ø and R at the extremes. The stability curve revealed that the integrator is not only A-stable, but also L- stable.
Keywords
Rational Integrator, Encroachment Point, Binomial Theorem, Absolute Stability, Jordan Curve, A-stable, L-Stability
Agbeboh Goddy Ujagbe, Ehiemua Michael Ebhodaghe, Loko Perelah, On the Stability Analysis of Rational Integrator Method for the Solution of Initial Value Problems in Ordinary Differential Equation, American Journal of Mathematical and Computer Modelling. Vol. 5, No. 4, 2020, pp. 102-108. doi: 10.11648/j.ajmcm.20200504.12
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