An evolutionary Newton procedure for solving nonlinear equations

T. Zhanlav   ; I. V. Puzynin

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 1, pp. 3-12

Bibliographie

[1] Gavurin M. K., “Nelineinye funktsionalnye uravneniya i nepreryvnye analogi iterativnykh metodov”, Izv. vuzov. Ser. matem., 1958, no. 5(6), 18–31 | MR | Zbl

[2] Zhidkov E. P., Makarenko G. I., Puzynin I. V., “Nepreryvnyi analog metoda Nyutona v nelineinykh zadachakh fiziki”, Fiz. elementarnykh chastits i at. yadra, 4:1 (1973), 127–165 | MR

[3] Zhidkov E. P., Khoromskii B. N., Nekotorye nelokalnye usloviya skhodimosti nepreryvnogo analoga metoda Nyutona, Preprint R5-8244, OIYaI, Dubna, 1974

[4] Zhidkov E. P., Khoromskii B. N., O lokalnoi skhodimosti priblizhennykh metodov resheniya operatornykh uravnenii, Preprint R5-9598, OIYaI, Dubna, 1976 | MR

[5] Puzynin I. V., Nepreryvnyi analog metoda Nyutona dlya chislennogo resheniya zadach kvantovoi mekhaniki, Avtoref. dis. ...dokt. fiz.-matem. nauk, OIYaI, Dubna, 1978; 11-12016

[6] Ermakov V. V., Kalitkin N. N., “Optimalnyi shag i regulyarizatsiya metoda Nyutona”, Zh. vychisl. matem. i matem. fiz., 21:2 (1981), 491–497 | MR | Zbl

[7] Melezhik V. S., Puzynin I. V., Puzynina T. P., Somov L. M., “Numerical solution of a system of integrodifferential equations arising from the quantum mechanical three-body problem with Coulomb interaction”, J. Comput Phys., 54:2 (1984), 221–236 | DOI | MR | Zbl

[8] Gareev F. A., Goncharov S. A., Zhidkov E. P. i dr., “Chislennye resheniya zadach na sobstvennye znacheniya dlya integrodifferentsialnykh uravnenii v teorii yadra”, Zh. vychisl. matem. i matem. fiz., 17:2 (1977), 407–419 | MR | Zbl

[9] Vinitsky S. I., Puzynin I. V., “Energy levels of mesic molecules”, J. Muon Catalyzed Fusion, 1988, no. 3, 307–320

[10] Blum E. K., Chang A. F., “A numerical method for the solution of the double eigenvalue problem”, J. Inst. Math. Appl., 22 (1978), 29–42 | DOI | MR | Zbl

[11] Vinitskii C. I., Gocheva A. D., Puzynin I. V., Iteratsionnaya skhema resheniya integro-differentsialnogo uravneniya na osnove variatsii parametra i metoda Nyutona, Preprint R11-81-837, OIYaI, Dubna, 1981

[12] Vinitskii S. I., Puzynin I. V., Smirnov Yu. S., “Reshenie zadach rasseyaniya na osnove mnogoparametricheskikh nyutonovskikh skhem. Odnokanalnoe rasseyanie”, Yadernaya fiz., 52:4(10) (1990), 1176–1189

[13] Davidenko D. F., “O prilozhenii metoda variatsii parametra k teorii nelineinykh funktsionalnykh uravnenii”, Ukr. matem. zhurnal, 7:1 (1955), 18–28 | MR | Zbl

[14] Kirzhnits D. A., Takibaev N. Zh., “Novyi podkhod v zadache trekh i bolee tel”, Yadernaya fiz., 25:3 (1977), 700–710

[15] Zhanlav T., Puzynin I. V., Chislennoe reshenie zadachi rasseyaniya s kompleksnym potentsialom, Preprint R11-89-643, OIYaI, Dubna, 1989 | MR

[16] Zhanlav T., Puzynin I. V., Mnogokanalnaya zadacha rasseyaniya v postanovke nelineinoi granichnoi zadachi, Preprint R11-90-382, OIYaI, Dubna, 1990 | MR

[17] Barashenkov I. V., Boyadjiev T. L., Puzynin I. V., Zhanlav T., “Stability of moving bubbles in a system of interacting bosons”, Phys. Letts A, 135:2 (1989), 125–128 | DOI

[18] Barashenkov I. V., Bogdan M. M., Zhanlav T., Instabilities and soliton structures in the driven nonlinear Schröedinger equation, Preprint E5-89-817, JINR, Dubna, 1989 | MR

[19] Kollatts L., Funktsionalnyi analiz i vychislitelnaya matematika, Mir, M., 1969

[20] Zhidkov E. P., Puzynin I. V., “Primenenie nepreryvnogo analoga metoda Nyutona dlya priblizhennogo resheniya odnoi nelineinoi granichnoi zadachi”, Dokl. AN SSSR, 180:1 (1968), 18–21 | Zbl

[21] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1980 | MR

[22] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[23] Dzh. Kholl, Dzh. Uatt (red.), Sovremennye chislennye metody resheniya obyknovennykh differentsialnykh uravnenii, Mir, M., 1979

[24] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[25] Marchuk G. I., Shaidurov V. V., Povyshenie tochnosti reshenii raznostnykh skhem, Nauka, M., 1979 | MR

[26] Aleksandrov L., “Regulyarizovannye vychislitelnye protsessy Nyutona-Kantorovicha”, Zh. vychisl. matem. i matem. fiz., 11:1 (1970), 36–43

[27] Aleksandrov L., “Regulyarizovannye traektorii priblizheniya nyutonovskogo tipa dlya resheniya nelineinykh uravnenii”, Differents. ur-niya, 13:7 (1977), 1281–1292 | MR | Zbl