Numerical Solution of a Parabolic Source Identification Problem with Involution and Neumann Condition

In this paper, a space source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. For the approximate solution of the problem, a stable difference scheme and its stability estimates are presented. The theoretical results are supported by the numerical results of a test problem. © 2021, Springer Nature Switzerland AG.