Software package for the numerical solution of systems of essentially nonlinear ordinary integro-differential-algebraic equations

N. G. Bandurin ; N. A. Gureeva

Matematičeskoe modelirovanie, Tome 24 (2012) no. 2, pp. 3-16.

Résumé

Method, algorithm and software package for automatic solution of ordinary non-linear integro-differential-algebraic equations (IDAE) of sufficiently general form is briefly described. Under the automatic solution the author understands getting result without executing the stages of selecting method, of programming and program checking. There are solved both initial and boundary tasks for such equations. It is assumed that the complete set of boundary and initial conditions at the beginning of interval of integration was set. In consequence of differentiation the system of IDAE can be modified into system of ordinary in common essentially non-linear differential equations (IDE). The problem of finding solving of the system mentioned above on the constant mesh of the interval of integration is posed in two forms — as solving of the system of IDAE and as solving of the appropriate system of IDE, where the developed program should be used. With the purpose of reducing of the system of IDAE and system of IDE to the systems of ordinary non-linear algebraic equations at every stage of solving in the algorithm integration formulas and differentiation formulas invented by the author are correspondingly used. Systems like those test systems of both non-linear IDAE and IDE, which were cited in this investigation, are solved by using of programmes. It is evident that coincidence of results of solving of one and the same system of equations in its different forms can serve as a good evidence of correctness of the results which are got.

Détail

Keywords: integral-differential-algebraic equations, numerical methods, nonlinear tasks, computer programs.

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