Geodesic
A class of one-step one-stage methods for stiff systems of ordinary differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1251-1265 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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M. V. Bulatov; A. V. Tygliyan; S. S. Filippov. A class of one-step one-stage methods for stiff systems of ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1251-1265. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a6/

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