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<p>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-difference 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.</p>

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PROJECTION-DIFFERENCE METHOD FOR APPROXIMATE SOLUTION OF A PARABOLIC EQUATION WITH NONLOCAL-IN-TIME CONDITION

  • 期刊论文

  • 发表日期：

    2026年2月1日

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

摘要

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-difference 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.