3 research outputs found
On a class of stationary loops on SO(n) and the existence of multiple twisting solutions to a nonlinear elliptic system subject to a hard incompressibility constraint
For full abstract please refer to http://dx.doi.org/10.1186/s13661-018-1047-
Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems
ูุธุฑุงู ูุฃูู
ูุชูุง ูู ุนููู
ุงูููุฒูุงุก ูุงูุฑูุงุถูุงุช ุงูุชุทุจูููุฉ ูุฅู ู
ุณุงุฆู ุดุชูุฑู
โ ูููููู ุบูุฑ ุงูุฎุทูุฉ ุดูุฏุช ุฅูุชู
ุงู
ุงู ู
ูุญูุธุงู ู
ูุฐ ุนุงู
1960. ูุงุญุฏุฉ ู
ู ุฃูู
ุงูุชูููุงุช ูู ุนูู
ุงูุฑูุงุถูุงุช ููู ุทุฑููุฉ ูููุชู - ูุงูุชุฑูููุชุด ุชู
ุชุทุจูููุง ูู ูุฐุง ุงูุจุญุซ ุนูู ูุงุญุฏู ู
ู ู
ุณุงุฆู ุดุชูุฑู
โ ูููููู ุบูุฑ ุงูุฎุทูุฉ. ุนูู ุญุฏ ุนูู
ุงูู
ุคูููู ููุฐุง ุงูุจุญุซ ูุฅู ุทุฑููุฉ ูููุชู - ูุงูุชุฑูููุชุด ูู
ูุณุจู ุฃู ุชู
ุชุทุจูููุง ูุญุฏ ุงูุขู ูุญู ูุฐุง ุงูููุน ุงูู
ูู
ู
ู ู
ุณุงุฆู ุดุชูุฑู
โ ูููููู ุบูุฑ ุงูุฎุทูุฉ ุงูุชู ูุชู
ู
ูุงูุดุฉ ุญููุง ูู ูุฐุง ุงูุจุญุซ. ูุจูุงุกู ุนูู ุฐูู ูุฅู ุงููุฏู ูู ูุฐุง ุงูุจุญุซ ูู ุชูุถูุญ ุฃู
ูุงููุฉ ุชุทุจูู ูุฐู ุงูุทุฑููุฉ ุงูู
ุนุฑููู ูุญู ูุฐุง ุงูููุน ุงูู
ูู
ู
ู ู
ุณุงุฆู ุดุชูุฑู
โ ูููููู ุบูุฑ ุงูุฎุทูุฉ. ููุชูุถูุญ ููุงุกุฉ ูุฐู ุงูุทุฑููุฉ ูู ุญู ูุฐุง ุงูููุน ู
ู ุงูู
ุณุงุฆู ููุฏ ุชู
ุนู
ู ู
ูุงุฑูุฉ ูู ูุฐุง ุงูุจุญุซ ุจูู ุชุทุจูู ุทุฑููุฉ ูููุชู โ ูุงูุชุฑูููุชุด ูุชุทุจูู ุทุฑููุฉ ุชุฌุฒุฆุฉ ุฃุฏูู
ูู ูุญู ุงูู
ุณุงุฆู ููุณูุง ุงูุชู ูุชูุงูููุง ูุฐุง ุงูุจุญุซ ูููุชูุฌุฉ ููุฐู ุงูู
ูุงุฑูุฉ ุชุจูู ุฃู ุงููุชุงุฆุฌ ุงูุชู ุญุตููุง ุนูููุง ู
ู ููุง ุงูุทุฑููุชูู ู
ุชูุงููู ู
ุน ุจุนุถูุง ุงูุจุนุถ.Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authorsโ knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by applying the well-known Newton-Kantorovich method. Also, to show the efficiency of applying this method to solve these problems, a comparison is made in this paper between the Newton-Kantorovich method and the Adomian decomposition method applied to the same non-linear Sturm-Liouville problems under consideration in this work. As a result of this comparison, the results of the Newton-Kantorovich method agreed with the results obtained by applying Adomianโs decomposition method