A New Class of A-stable Implicit Schemes for Treatment of Stiff System of Ordinary Differential Equations

P.O. Babatola

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A New Class of A-stable Implicit Schemes for Treatment of Stiff System of Ordinary Differential Equations

机译：一类新的A-稳定隐式格式处理常微分方程的刚性系统

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In this paper, a new class of A-Stable Implicit Rational Runge-Kutta schemes were developed, analyzed and computerized to solve stiff system of ordinary differential equations. The method is motivated by the Implicit Conventional Runge – Kutta Schemes and Rational function approximation. While its development and analyses make use of Taylor series expansion (Taylor and Binomial) and Pade’s approximation techniques respectively. The schemes are convergent and A-stable.

机译：本文开发，分析和计算机化了一类新型的A稳定隐式有理Runge-Kutta方案，以求解常微分方程的刚性系统。该方法受隐式常规Runge – Kutta方案和有理函数逼近的启发。它的开发和分析分别使用泰勒级数展开式（泰勒和二项式）和帕德的逼近技术。该方案是收敛的和A稳定的。

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《Mathematical Theory and Modeling》 |2013年第1期|共10页
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P.O. Babatola;
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1. Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff ito stochastic differential equations Mean-square A-stable diagonally drift-implicit integrators of weak [J] . A. Abdulle, G. Vilmart, K.C. Zygalakis BIT numerical mathematics . 2013,第4期

机译：刚性itto随机微分方程的弱二阶均方A稳定对角漂移隐积分
2. A Family of Continuous Blended Block A-Stable Second Derivative Linear Multistep Methods for the solutions of Stiff System of Ordinary Differential Equations [J] . Omagwu Samson, J. P. Chollom, G. M. Kumleng, British Journal of Mathematics & Computer Science . 2018,第6期

机译：常微分方程刚性系统解的一类连续混合块A-稳定二阶导数线性多步方法
3. A-stable and Stiffly-stable Formulas in Generalized Linear Multistep Methods for Ordinary Differential Equations [J] . KEN-ICHIRO MITSUDA, CHISATO SUZUKI 情報処理学会論文誌 . 2004,第1期

机译：常微分方程的广义线性多步法中的A稳定和刚性稳定公式
4. A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations [C] . H. Musa, M.B. Suleiman, F. Ismail International Conference on Research and Education in Mathematics . 2012

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5. Stiff ordinary and delay differential equations in biological systems. [D] . Caberlin, Martin D. 2002

机译：生物系统中的常微分方程和时滞微分方程。
6. Contribution to Speeding-Up the Solving of Nonlinear Ordinary Differential Equations on Parallel/Multi-Core Platforms for Sensing Systems [O] . Vahid Tavakkoli, Kabeh Mohsenzadegan, Jean Chamberlain Chedjou, 2020

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7. A-stable one-step methods with step-size control for stiff systems of ordinary differential equations [O] . Alt René 1978

机译：常态微分方程刚性系统的带步长控制的稳定一步法
8. Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients. [R] . Sun, J., Jackson, K. 1982

机译：求解具有陡梯度的常微分方程初值问题的非线性隐式一步格式。

A New Class of A-stable Implicit Schemes for Treatment of Stiff System of Ordinary Differential Equations

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