The Difference Problem of Obtaining the Parameter of a Parabolic Equation

Abstract

The boundary value problem of determining the parameter $p$ of a parabolic equation ${\upsilon }^{\prime }(t)+A\upsilon (t)=f(t)+p(0\le t\le 1),\upsilon (0)=\phi ,\upsilon (1)=\psi$ in an arbitrary Banach space $E$ with the strongly positive operator $A$ is considered. The first order of accuracy stable difference scheme for the approximate solution of this problemis investigated. The well-posedness of this difference scheme is established. Applying the abstract result, the stability and almost coercive stability estimates for the solution of difference schemes for the approximate solution of differential equations with parameter are obtained.