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Modifications to a Runge-Kutta-type software package for the numerical solution of boundary value ordinary differential equations.

机译：对Runge-Kutta型软件包的修改，以求取边值常微分方程的数值解。

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MIRKDC [Enright, Muir, 1996] is a software package for the numerical solution of systems of first order, nonlinear, boundary value ordinary differential equations (ODEs), with separated boundary conditions. It employs mono-implicit Runge-Kutta methods for the discretization of the ODEs and monitors the quality of the numerical solution using defect control. The discrete systems are solved by modified Newton iterations and extensive use of adaptive mesh refinement is employed.;This thesis describes modifications to the MIRKDC software package in order to incorporate a number of performance enhancements including computational derivative approximation, analytic derivative assessment, problem sensitivity (conditioning) assessment, introduction of new optimized Runge-Kutta formulas, improvement of the defect control strategy and the introduction of an auxiliary global error indicator. Numerical results to demonstrate the impact of these enhancements are presented.

机译：MIRKDC [Enright，Muir，1996]是一个用于求解一阶非线性，边界值为常微分方程（ODE）且具有独立边界条件的系统的数值解的软件包。它使用单隐Runge-Kutta方法离散化ODE，并使用缺陷控制监控数值解的质量。通过修改的牛顿迭代法解决离散系统问题，并广泛使用自适应网格细化方法。;本文描述了对MIRKDC软件包的修改，以便合并许多性能增强功能，包括计算导数逼近，解析导数评估，问题敏感性（评估），引入新的优化Runge-Kutta公式，改进缺陷控制策略以及引入辅助全局误差指标。数值结果证明了这些增强的影响。

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作者
Xu, Hui.;
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作者单位

Saint Mary's University (Canada).;

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授予单位 Saint Mary's University (Canada).;
学科 Computer Science.;Mathematics.
学位 M.Sc.
年度 2004
页码 90 p.
总页数 90
原文格式 PDF
正文语种 eng
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专利

1. A Method and a Software Package for Numerical Solution of the Systems of Nonlinear Ordinary Integro-Differential-Algebraic Equations [J] . N. G. Bandurin, N. A. Gureeva Mathematical models and computer simulations . 2012,第5期

机译：非线性普通积分-微分-代数方程组数值解的方法和软件包
2. THE COLLOCATION METHOD IN THE NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS. PART II: DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS [J] . Maset S. SIAM Journal on Numerical Analysis . 2015,第6期

机译：中立型泛函微分方程边值问题数值解的集合方法。第二部分：具微分方程的微分方程
3. THE COLLOCATION METHOD IN THE NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS. PART I: CONVERGENCE RESULTS [J] . Maset S. SIAM Journal on Numerical Analysis . 2015,第6期

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4. The numerical solutions for stiff ordinary differential equations by using interpolated variational iteration method with comparison to exact solutions [C] . Cihan Ciftci, Hatice Sinem Sas Cayci, Mehmet Tarik Atay, International Conference of Numerical Analysis and Applied Mathematics . 2018

机译：与精确解决方案相比，使用内插改性方法使用插值变分迭代方法来实现常规差分方程的数值解
5. Twin solutions of even order boundary value problems for ordinary differential equations and finite difference equations. [D] . Sun, Xun. 2009

机译：常微分方程和有限差分方程偶数边值问题的孪生解。
6. Searching fundamental information in ordinary differential equations. Nondimensionalization technique [O] . J. F. Sánchez Pérez, M. Conesa, I. Alhama, -1

机译：在常微分方程中搜索基本信息。无量纲化技术
7. I. Asymptotic boundary conditions for ordinary differential equations. II. Numerical Hopf bifurcation [O] . Jepson Allan Douglas 1981

机译：I.常微分方程的渐近边界条件。 II。数值Hopf分岔
8. SOLVEBLOK: A Package for Solving Almost Block Diagonal Linear Systems, with Applications to Spline Approximation and the Numerical Solution of Ordinary Differential Equations. [R] . de Boor, C., Weiss, R. 1976

机译：sOLVEBLOK：解决几乎块对角线性系统的一种包，应用于样条逼近和常微分方程的数值解。

Modifications to a Runge-Kutta-type software package for the numerical solution of boundary value ordinary differential equations.

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