This article is cited in 2 papers

An iterative method for solving an inverse problem for a first-order nonlinear partial differential equation with estimates of guaranteed accuracy and the number of steps

D. V. Churbanov, A. Yu. Shcheglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: For a partial differential equation simulating population dynamics, the inverse problem of determining its nonlinear right-hand side from an additional boundary condition is studied. This inverse problem is reduced to a functional equation, for which the existence and uniqueness of a solution is proven. An iterative method for solving this inverse problem is proposed. The accuracy of the method is estimated, and restrictions on the number of steps are obtained.

Key words: inverse problem, functional equation, existence and uniqueness of solution.

UDC: 519.63

Received: 05.04.2012
Revised: 05.06.2012

DOI: 10.7868/S0044466913020063

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:2, 215–220

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•