Approximate solution of a parabolic equation with the use of a rational approximation to the operator exponential (Q2358838)

The author proposes a solution method for the parabolic equation \(dx/dt=Bx+bv(t)\) with an unbounded self-ad joint operator \(B\). Here \(b\) is a vector and \(v(t)\) is a scalar function. A series approximation to the fundamental solution of this problem is constructed. The method is illustrated by an example of inhomogeneous heat equations. Also, an a priori error estimate is obtained. Several theorems are proved.