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首页> 外文期刊>Mathematical models and computer simulations >A Method and a Software Package for Numerical Solution of the Systems of Nonlinear Ordinary Integro-Differential-Algebraic Equations
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A Method and a Software Package for Numerical Solution of the Systems of Nonlinear Ordinary Integro-Differential-Algebraic Equations

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

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摘要

A method, an algorithm and a software package for automatically solving the ordinary nonlinear integro-differential-algebraic equations (IDAEs) of a sufficiently general form are described. The author understands an automatic solution as obtaining a result without carrying out the stages of selecting a method, programming, and program checking. Both initial and boundary value problems for such equations are solved. It is assumed that the complete set of boundary and initial conditions at the beginning of the integration interval are given. By performing differentiation, the system of IDAEs can be modified, in general, into a system of ordinary nonlinear differential equations (IDEs). The problem of finding the solution of the above-mentioned system on the uniform grid on the integration interval is posed in two forms: as solving the system of IDAEs and as solving the appropriate system of IDEs, where the developed program is to be used. In order to reduce the system of IDAEs and the system of IDEs to the systems of ordinary nonlinear algebraic equations, at every stage of the algorithm the integration and differentiation formulas obtained earlier by N.G. Bandurin are used. Systems similar to those test systems of both nonlinear IDAEs and IDEs considered in this investigation are solved by using the computer programs. It is evident that the coincidence of the results for one and the same system of equations in its different forms can serve as good evidence of the correctness of the obtained results.
机译：描述了一种用于自动求解足够通用形式的普通非线性积分微分代数方程（IDAE）的方法，算法和软件包。作者将自动解决方案理解为无需执行选择方法，编程和程序检查阶段的结果即可获得结果。此类方程的初值和边值问题都可以解决。假设在积分间隔开始时给出了完整的边界条件和初始条件。通过执行微分，通常可以将IDAE的系统修改为普通非线性微分方程（IDE）的系统。在积分间隔上的均匀网格上找到上述系统的解决方案的问题有两种形式：解决IDAE系统和解决适当的IDE系统（要使用开发的程序）。为了将IDAE的系统和IDE的系统简化为普通的非线性代数方程式的系统，在算法的每个阶段，NG早先获得了积分和微分公式。使用班杜林。通过使用计算机程序可以解决与本次调查中考虑的非线性IDAE和IDE测试系统相似的系统。显然，一个方程组和一个方程组的不同形式的结果的符合性可以很好地证明所获得结果的正确性。

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