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ВИКОРИСТАННЯ СКМ MAPLE ДЛЯ ВІЗУАЛІЗАЦІЇ НАБЛИЖЕНИХ РОЗВ’ЯЗКІВ ДИФЕРЕНЦІАЛЬНИХ РІВНЯНЬ ЗА ОДНОКРОКОВИМ МЕТОДОМ ЕЙЛЕРА

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Олена С., Володимир Ш.
Педагогічні науки: теорія, історія, інноваційні технології
|
2017
|
issue 3(67)
246-257
EN
Purpose. The article deals with the question of visualization of approximate solutions of differential equations by the one-step Euler method in the computer mathematics system MAPLE. Methods: theoretical (analysis and systematization of research literature, works of local and foreign authors, teaching materials in the context of using of instruments SCA MAPLE); empirical (research and summarizing the experience of using SCA MAPLE in the same calculations to solving applied and mathematical problems), on the basis of which effective ways of using computer tools for visualizing SCM MAPLE approximate solutions of differential equations for the one-step method Euler are determined. Results: The importance of mastering the basic ideas of finding solutions of differential equations solvable with respect to the derivative at the level of visualization of integral curves is substantiated. The general formulation of the problem is described, the requirements imposed on the function are given, so that the one-step Euler method is applied. The possibility of using the computer toolkit SCA MAPLE is demonstrated. The importance of a visual approach to the study of numerical methods for solving differential equations and estimating the errors of such approximations is emphasized. Conclusions: MAPLE use specialized package not only simplifies and accelerates cumbersome calculation of the function at the nodes, but also allows you visualizing this approach. This visualization contributes to a better assimilation methods for solving differential equations solved relatively derivative and the formation of mathematical skills to use computer environment in professional activities during other classes of solving mathematical problems. The directions offurther researches are seen in the study of principles of forming professional readiness to use computer visualization tools of mathematical knowledge.
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