Сходимость сеточно-интерполяционных аппроксимаций решения квазилинейной параболической краевой задачи на отрезке

We consider the one-dimensional quazi-linear parabolic Neumann boundary value problem: coeffcients of the partial differential equation and right-hand sides of the boundary conditions depend on time, point, and the history of the solution. Convergence of difference approximations to a weak solution to the problem is proved.