Geodesic
Approximation of the Jacobi matrix in $(m,3)$-methods of solving stiff systems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 3, pp. 283-295

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The theorem that the maximal order of accuracy of $L$-stable $(m,k)$-methods with freezing the Jacobi matrix is equal to four. 
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     author = {A. L. Dvinsky and E. A. Novikov},
     title = {Approximation of the {Jacobi} matrix in $(m,3)$-methods of solving stiff systems},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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A. L. Dvinsky; E. A. Novikov. Approximation of the Jacobi matrix in $(m,3)$-methods of solving stiff systems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 3, pp. 283-295. http://geodesic.mathdoc.fr/item/SJVM_2008_11_3_a3/