An abstract framework in the numerical solution of boundary value problems for neutral functional differential equations (Q726721)

The boundary value problem for functional differential equation of the form \[ y^{\prime}(t) = F(t,y,y^{\prime},p),\qquad t\in [a,b], \] \[ B( y,y^{\prime},p )=0 \] is presented in the abstract form \[ y^{\prime} = \mathbf{F} ( y,y^{\prime},p) \] in an abstract Banach space \(\mathbf{U}\). Using the process of discretization, this form is reduced to a problem of a fixed point in a finite-dimensional space. The convergence of the solutions of this problem to the exact solution is proved, imposing several supplementary conditions on the data of the problem. Numerical illustration of the results is absent.