Alternating order algorithm based on stages of Ceschino’s method

Тип публикации: статья из журнала

Год издания: 2013

Ключевые слова: explicit methods, control accuracy and stability, stiff problems

Аннотация: This paper investigates the methods for numerical solution of stiff problems with large dimension. Using the estimation of the largest eigenvalue of the Jacobi matrix it has been constructed an inequality in order to control the stability of a Cescino numerical scheme with second-order accuracy. To integrate a variable step it is proposed a formula which allows predicting the next step in time. On the basis of this formula, it has been developed a method with first-order accuracy with extended stability range. This method allows stabilize behavior of step integration at the stage of solution exactly where stability plays a crucial role. This makes it possible to remove restrictions on the possibility of using explicit methods for solving stiff problems. It has been formulated an algorithm for the numerical solution of stiff problems of variable order, which uses the irregular step in time with an additional control of stability of the numerical integration scheme. This paper demonstrates solutions of stiff problems associated with numerical simulations of ethane pyrolysis, which confirm an increase in efficiency due to the use of variable order.

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Журнал: Tyumen State University Herald

Выпуск журнала: 7

Номера страниц: 103-110

ISSN журнала: 23076445

Место издания: Тюмень

Издатель: Федеральное государственное автономное образовательное учреждение высшего образования «Тюменский государственный университет»


  • Novikov E.A. (Institute of Computational Modeling, Siberian Branch of Russian Academy of Science)
  • Zakharov Alexander A. (Tyumen State University)

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