Geodesic
Numerical methods based on multipoint Hermite interpolating polynomials for solving the Cauchy problem for stiff systems of ordinary differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 234-244

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Families of $A$-, $L$- and $L(\delta)$-stable methods are constructed for solving the Cauchy problem for a system of ordinary differential equations (ODEs). The $L(\delta)$-stability of a method with a parameter $\delta\in(0,1)$ is defined. The methods are based on the representation of the right-hand sides of an ODE system at the step $h$ in terms of two-or three-point Hermite interpolating polynomials. Comparative results are reported for some test problems. The multipoint Hermite interpolating polynomials are used to derive formulas for evaluating definite integrals. Error estimates are given. 
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     author = {A. F. Latypov and Yu. V. Nikulichev},
     title = {Numerical methods based on multipoint {Hermite} interpolating polynomials for solving the {Cauchy} problem for stiff systems of ordinary differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
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     number = {2},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a6/}
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A. F. Latypov; Yu. V. Nikulichev. Numerical methods based on multipoint Hermite interpolating polynomials for solving the Cauchy problem for stiff systems of ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 234-244. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a6/