A finite-difference interpretation of a nonlocalproblem with a parameterised first-order differential equation - Dovletov, Dovlet M. (Journal of the Belarusian State University. Mathematics and Informatics, 2025)
In this work the nonlocal initial value problem and corresponding finite-difference interpretation for the first-order linear ordinary differential equation with a parameter at the derivative is studied. The nonlocal initial value condition is given by terms of multipoint linear combination. The difference scheme with exponential fit is proposed on a uniform mesh. The article identifies the requirements on the location of nonlocal data carriers in the multipoint condition, on the values of corresponding coefficients and on the parameter variation interval, under which a uniform on parameter stability of classical and difference solutions, as well as a uniform on parameter convergence of difference solution to classical solution are proved. The identification and proof of such conditions, which provide a uniform on parameter approximation of the nonlocal initial value problem classical solution by the solution of exponentially fitted difference scheme, define the novelty of the current work.