МЕТОД ДВОБІЧНИХ НАБЛИЖЕНЬ У ЧИСЕЛЬНОМУ АНАЛІЗІ ЗАДАЧІ ДІРІХЛЕ ДЛЯ НЕЛІНІЙНОГО РІВНЯННЯ ТЕПЛОПРОВІДНОСТІ

A one-dimensional Dirichlet problem for the heat equation with an expo-nential heat conductivity coefficient and a heat sources function is considered. By replacing the unknown function, the problem under consideration was re-duced to a problem for a semilinear differential equation, which was analyzed by methods of the operators theory in semi-ordered Banach spaces. Conditions for the existence of a single positive solution are obtained. The results of a com-putational experiment are presented.