A class of one-step one-stage methods for stiff systems of ordinary differential equations |
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Authors: | M V Bulatov A V Tygliyan S S Filippov |
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Institution: | 1.Institute of System Dynamics and Control Theory, Siberian Branch,Russian Academy of Sciences,Irkutsk,Russia;2.Keldysh Institute of Applied Mathematics,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | 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. |
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