Abstract. We obtain the improved error estimates of the finite-difference scheme for a two-dimensional parabolic equation in a unit square, considering the effect of the Dirichlet boundary condition and the initial condition. We prove that the accuracy order is higher near the sides and the bottom of the space-time parallelepiped.
Keywords: parabolic equation, initial-boundary problem, finite-difference scheme, error estimate, boundary and initial effects.
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
e-mail: natmaiko@gmail.com.