Geodesic
Three- and four-step implicit absolutely stable fourth-order Runge–Kutta schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 116-130 
V. I. Pinchukov. Three- and four-step implicit absolutely stable fourth-order Runge–Kutta schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 116-130. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_1_a11/
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     title = {Three- and four-step implicit absolutely stable fourth-order {Runge{\textendash}Kutta} schemes},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two types of implicit fourth-order Runge–Kutta schemes are constructed for first-order ordinary differential equations, multidimensional transfer equations, and compressible gas equations. The absolute stability of the schemes is proved by applying the principle of frozen coefficients. Adaptive artificial viscosity ensuring good time convergence and oscillations damping near discontinuities is used in solving gas dynamics equations. The comparative efficiency of the schemes is illustrated by numerical results obtained for compressible gas flows.

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