Study and numerical solution of a class of coefficient-inverse problems for ODEs with nonlocal conditions

Abstract We study a class of problems in which unknown constant coefficients appear in the free terms of non-autonomous systems of ordinary differential equations and must be identified. The basic and additional (overdetermining) conditions are, in general, nonlocal. They involve cumulative information about the state functions, including their values at selected points and their integrals over given subintervals. Depending on how the number of unknown coefficients compares with the number of additional conditions, different problem formulations and corresponding solution methods are discussed. We also present results of numerical experiments and analyze how errors in the given conditions influence the accuracy of the computed solutions for test problems.