A Numerical Algorithm for Solving Stiff Ordinary Differential Equations

S. A. M. Yatim; Z. B. Ibrahim; K. I. Othman; M. B. Suleiman

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A Numerical Algorithm for Solving Stiff Ordinary Differential Equations

机译：求解刚性常微分方程的数值算法

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An advanced method using block backward differentiation formula (BBDF) is introduced with efficient strategy in choosing the step size and order of the method. Variable step and variable order block backward differentiation formula (VSVO-BBDF) approach is applied throughout the numerical computation. The stability regions of the VSVO-BBDF method are investigated and presented in distinct graphs. The improved performances in terms of accuracy and computation time are presented in the numerical results with different sets of test problems. Comparisons are made between the proposed method and MATLAB's suite of ordinary differential equations (ODEs) solvers, namely, odel5s and ode23s.

机译：介绍了一种使用块后向微分公式（BBDF）的高级方法，该方法具有有效的策略来选择方法的步长和顺序。在整个数值计算中都采用了可变步长和阶数可变的块后向微分公式（VSVO-BBDF）。研究了VSVO-BBDF方法的稳定性区域，并在不同的图中显示。在具有不同测试问题集的数值结果中，在准确性和计算时间方面表现出了改进的性能。比较了所提出的方法和MATLAB的一组常微分方程（ODE）求解器，即odel5s和ode23s。

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来源
《Mathematical Problems in Engineering》 |2013年第1期|989381.1-989381.11|共11页
作者
S. A. M. Yatim; Z. B. Ibrahim; K. I. Othman; M. B. Suleiman;
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School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia;

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Selangor, 40450 Shah Alam, Malaysia;

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

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1. A Numerical Algorithm for Solving Stiff Ordinary Differential Equations [J] . S. A. M.Yatim, Z. B.Ibrahim, K. I.Othman, Mathematical Problems in Engineering: Theory, Methods and Applications . 2013,第2期

机译：求解刚性常微分方程的数值算法
2. An Adaptive Time-Step Backward Differentiation Algorithm to Solve Stiff Ordinary Differential Equations: Application to Solve Activated Sludge Models [J] . Jamal Alikhani, Bahareh Shoghli, Ujjal Kumar Bhowmik, American Journal of Computational Mathematics . 2016,第4期

机译：求解刚性常微分方程的自适应时步向后微分算法：在活性污泥模型求解中的应用
3. A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations [J] . S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, Mathematical Problems in Engineering . 2011,第PTa3期

机译：求解常微分方程的数值方法的定量比较
4. Solving some ordinary differential equations numerically using differential evolution algorithm with a simple adaptive mutation scheme [C] . Werry Febrianti, Kuntjoro Adji Sidarto, Novriana Sumarti International Conference on Mathematics, Computational Sciences and Statistics . 2020

机译：用简单的自适应突变方案用差分演化算法在数值上进行数值求解一些常微分方程
5. Validated numerical bounds on the global error for initial value problems for stiff ordinary differential equations. [D] . Yu, Chao. 2004

机译：刚性常微分方程初值问题全局误差的有效数值界。
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

机译：用于加速对照对传感系统并行/多核平台的非线性常微分方程的贡献
7. A Numerical Algorithm for Solving Stiff Ordinary Differential Equations [O] . Yatim S. A. M., Ibrahim Z. B., Othman K. I., 2012

机译：求解刚性常微分方程的数值算法

A Numerical Algorithm for Solving Stiff Ordinary Differential Equations

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