Geodesic
A variable structure algorithm using the (3,2)-scheme and the Fehlberg method
Numerical methods and programming, Tome 16 (2015) no. 3, pp. 446-455

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A third-order (3,2)-method allowing freezing the Jacobi matrix is constructed. Its main and intermediate numerical schemes are $L$-stable. An accuracy control inequality is obtained using an embedded method of second order. A stability control inequality for the explicit three-stage Runge-Kutta-Fehlberg method of third order is proposed. A variable structure algorithm is formulated. An explicit or $L$-stable method is chosen according to the stability criterion at each step. Numerical results are discussed.
Mots-clés : (m, variable structure algorithm
Keywords: stiff systems, (m,k)-schemes, Fehlberg method, Runge-Kutta methods, accuracy and stability control, ordinary differential equations, numerical methods. 
@article{VMP_2015_16_3_a10,
     author = {E. A. Novikov},
     title = {A variable structure algorithm using the (3,2)-scheme and the {Fehlberg} method},
     journal = {Numerical methods and programming},
     pages = {446--455},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_3_a10/}
}
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E. A. Novikov. A variable structure algorithm using the (3,2)-scheme and the Fehlberg method. Numerical methods and programming, Tome 16 (2015) no. 3, pp. 446-455. http://geodesic.mathdoc.fr/item/VMP_2015_16_3_a10/