Construction of approximate solutions of boundary value problems for ordinary differ-ential equations in the form of trigonometric polynomials

Authors

  • В. П. Денисюк Національний авіаційний університет
  • Л. В. Рибачук Національний авіаційний університет
  • О. В. Негоденко Національний авіаційний університет

DOI:

https://doi.org/10.18372/2073-4751.1.7694

Keywords:

тригонометричний многочлен, вузлові точки, нев’язка, явище Гіббса, фантомні вузли

Abstract

There was suggested a method of constructing approximate solutions of the first boundary problem for ordinary differential equations of the second order with variable coefficients in trigonometric polynomials using the phantom nodes method. Unknown parameters are determined by collocation. An example is given; it is shown that the relative error of the solution has reduced in 3.7 times with the introduction of two phantom nodes and in 6 times with the introduction of four phantom nodes

Author Biographies

В. П. Денисюк, Національний авіаційний університет

д.ф.-м.; проф

Л. В. Рибачук, Національний авіаційний університет

к.ф.-м.; доц

References

Дзядык В. К. Введение в теорию равномерного приближения функций полиномами. – Наука, М., 1977. – 512 с.

Хемминг Р.В. Численные методы. – М., 1968 г. – 400 с.

Денисюк В.П. О некоторых методах улучшения сходимости тригонометрических рядов Фурье и интерполяционных тригонометрических многочленов//Journal of Qafqaz University, Mathematics and Computer Science, Number 33 (2012), http://journal.qu.edu.az.

Флетчер К. Численные методы на основе метода Галеркина – М.: Мир, 1988. – 352 с.

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Published

2014-03-29

How to Cite

Денисюк, В. П., Рибачук, Л. В., & Негоденко, О. В. (2014). Construction of approximate solutions of boundary value problems for ordinary differ-ential equations in the form of trigonometric polynomials. Problems of Informatization and Management, 1(45), 37–41. https://doi.org/10.18372/2073-4751.1.7694

Issue

Vol. 1 No. 45 (2014)

Section

Статті

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