Fourth-order diagonally implicit schemes for evolution equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1080-1084
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New fourth-order methods are proposed for solving both ordinary and partial differential equations. The derivation of the methods is based on the form of diagonally implicit schemes applied to stiff ordinary differential equations. The methods are absolutely and unconditionally stable. Test computations are presented.
[1] Dzh. Kholl, Dzh. Uatt (red.), Sovremennye chislennye metody resheniya obyknovennykh differentsialnykh uravnenii, Mir, M., 1979
[2] Dekker K., Verver Ya., Ustoichivost metodov Runge–Kutty dlya zhestkikh nelineinykh differentsialnykh uravnenii, Mir, M., 1988 | MR
[3] Shirobokov N. V., “Diagonalno-neyavnye skhemy Runge–Kutty”, Zh. vychisl. matem. i matem. fiz., 42:7 (2002), 1013–1018 | MR | Zbl
[4] Shirobokov N. V., “Rasscheplenie evolyutsionnykh uravnenii na osnove diagonalno-neyavnykh metodov tretego poryadka”, Zh. vychisl. matem. i matem. fiz., 45:2 (2005), 262–266 | MR | Zbl