Reciprocal Function Method for Cauchy Problems with First-Order Poles

Abstract: For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to continue the solution through the poles and to determine the solution and the pole positions with good accuracy. The method allows one to employ conventional explicit and implicit schemes, for example, explicit Runge–Kutta schemes. A test problem with multiple poles is computed as an example. The proposed method is useful for construction of software for direct computation of special functions. © 2020, Pleiades Publishing, Ltd.

Авторы
Журнал
Номер выпуска
2
Язык
Английский
Страницы
165-168
Статус
Опубликовано
Том
101
Год
2020
Организации
  • 1 Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russian Federation
  • 2 RUDN University, Moscow, 117198, Russian Federation
  • 3 Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russian Federation
Ключевые слова
Cauchy problem; continuation through a pole; singularities
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/64933/