The modified successive approximations method and Padé approximants for solving the differential equation with variant retarded argument
In order to approximate the solution of the boundary-value problem for a linear second-order delay differential equation, \[ \begin{gathered} x''(t)+ a(t) x(t-\tau))= f(t),\quad t\in [0,T],\\ x(t)= \varphi(t),\quad t\leq 0,\quad x(T)= x_T,\end{gathered} \] the authors convert the problem into a mixed (Fredholm-Volterra type) integral equation. Approximations to \(x\) are then obtained by iterative techniques based on successive approximation and series of Padé approximants. A test problem illustrates the method.
linear second-order delay differential equation
scientific article; zbMATH DE number 2081696