One-step methods for retarded differential equations with parameters (Q582023)

The numerical solution of delay differential equations with parameters is considered. More precisely, the problem under consideration is to seek a real function y(t) defined on an interval \([a,b]=I\) and the value of a parameter \(\lambda\), such that they satisfy the differential equation: \(y'(t)=f(t,y(t),y(\alpha (t)),6l),\) \(t\in I\), and the boundary conditions \(y(t)=g(t),\) \(t\leq a\), \(M\lambda +Ny(b)=K.\) Assuming that the problem has a unique solution, a one-step iterative method is proposed and under some conditions, it is proved that it converges to the true solution. Several examples are used to check numerically the convergence of the above method.