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A class of one-step one-stage methods for stiff systems of ordinary differential equations

Авторы: Bulatov M.V., Tygliyan A.V., Filippov S.S.

Журнал: Computational Mathematics and Mathematical Physics

Том: 51

Номер: 7

Год: 2011

Отчётный год: 2011

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Аннотация: A new class of one-step one-stage methods (ABC-schemes) designed for the numerical solution of stiff initial value problems for ordinary differential equations is proposed and studied. The Jacobian matrix of the underlying differential equation is used in ABC-schemes. They do not require iteration: a system of linear algebraic equations is once solved at each integration step. ABC-schemes are A- and L-stable methods of the second order, but there are ABC-schemes that have the fourth order for linear differential equations. Some aspects of the implementation of ABC-schemes are discussed. Numerical results are presented, and the schemes are compared with other numerical methods.

Индексируется WOS: 1

Индексируется Scopus: 0

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