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doi: 10.5281/zenodo.8427
Аппроксимационно-операционный подход применен к решению интегральных уравнений Фредгольма и Вольтерра второго рода. Показано, что аппроксимация ядер интегральных уравнений как сигналов, зависящих от двух аргументов, обобщенными полиномами на основе двумерных базисных функций блочно-импульсного типа позволяет алгебраизировать интегральные уравнения. Приведены примеры, иллюстрирующие применение подхода в программной среде системы Mathematica® --- О. V. Vasyliev, V. V. Vasylyev, L. A. Simak Approximative solution of integral Fredholm and Volterra equations of the second kind by Stransform Approximative-operational approach is applied to the solution of integral equations of Fredholm and Volterra second kind. It is shown that the approximation of the kernels of integral equations as a signals dependent of two arguments, via generalized polynomials on the basis of two-dimensional basis functions of block-pulse type allows to obtain the algebraizable form of integral equations. Computer experiments are completed via programming environment of Mathematica ®.
операционное исчисление, интегральные уравнения Фредгольма и Вольтерра, динамическая система, математическое моделирование, S-преобразования
операционное исчисление, интегральные уравнения Фредгольма и Вольтерра, динамическая система, математическое моделирование, S-преобразования
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