The longitudinal scheme of the method of lines for the numerical approximation of boundary value problems with nonsmooth data for a differential equation of second order of parabolic type.
Malevanny I.I., Karjakin Т.I.
The study of boundary value problems for parabolic equations is one of the classic problems of the theory of differential equations with partial derivatives and causes continuing interest of mathematicians. The reason for this is the exceptional practical importance of parabolic equations, which finds application in various applied areas of science. Boundary value problems with nonsmooth data for a differential equation of second order of parabolic type are a difficult object of study both from the theoretical point of view, and from the point of view of developing numerical methods for approximating the solution of such problems. The present work describes the construction and software implementation of the numerical method of lines using the generalized formulation and application of Steklov averaging operators.
