The talk is devoted to an application of the modified
F-transform technique for solving linear boundary value
problems via the collocation method. An approximate solution
is sought as the inverse F-transform of some discrete
function. Applying the technique of F-transform for
numerical solving differential equations with boundary
conditions, it is important to guarantee high quality of
approximation on the whole interval under consideration and
especially near the boundary points. The aim of the proposed
modification of F-transform is to introduce a technique
which allows to extend good approximation properties of the
previously introduced spline-based F-transform from the
interval where the Ruspini condition is fulfilled to the
whole interval under consideration. Such modification is
important for applications and allows to use the advantages
of spline-based F-transforms in collocation.