Construction of the solutions of difference equations in the field of Mikusiński operators
The difference equation (i) \(a_nu_{n-1}+ b_nu_n+ c_nu_{n+1}= f_n\), \(n= 1,\dots, N-1\), is solved for given boundary values \(u_0\), \(u_N\) in the following case: The coefficients are continuous operator functions, and the boundary values are operators, both in the field of Mikusiński. The authors discuss, whether the solutions are continuous functions, or at least continuous operator functions, or not. In the case that (i) is the discretization of a differential equation, the error between the solutions is estimated.
scientific article; zbMATH DE number 1206699