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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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[8] Dvinskii A. L., Issledovanie (m, k)-metodov s $L$-ustoichivymi promezhutochnymi skhemami dlya resheniya zhestkikh zadach, Diss. $\dots$ kand. fiz.-mat. nauk: 01.01.07, Krasnoyarsk, 2004

[9] Novikov E. A.,Shitov Yu. A., Algoritm integrirovaniya zhestkikh sistem na osnove (m, k)-metoda vtorogo poryadka tochnosti s chislennym vychisleniem matritsy Yakobi, Preprint / VTs SO RAN No 20, Krasnoyarsk, 1988

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