Projection-difference method for approximate solution of a parabolic equation with nonlocal-in-time condition

A. A. Petrova, D. V. Gribanov, A. S. Bondarev

Voronezh State University

Abstract: We consider a parabolic equation with a nonlocal-in-time condition on solution in a separable Hilbert space. This problem is solved approximately by the projection-dfference method using the implicit Euler method in time. An estimate of the approximate solution is obtained. Estimates of errors of approximate solutions are established, the convergence of approximate solutions to the exact solution is proved, and the convergence rate is estimated.

Keywords: Hilbert space, parabolic equation, nonlocal condition, projection-difference method, implicit Euler method

UDC: 517.954

MSC: 58D25, 35Kxx

DOI: 10.36535/2782-4438-2025-245-65-77