The ordinary successive approximations method and Padé approximants for solving a differential equation with variant retarded argument (Q1398665)

The authors present a numerical method to solve boundary value problems for differential equations with retarded argument. At first they derive a Fredholm-Volterra integral equation which is equivalent to the original differential problem. Then the existence and uniqueness of solution is proved together with convergence of successive approximations, defined by a Green function. At last, it is shown that the use of Padé series provides numerical stability. An interesting example is numerically solved, to support the previoulsy presented theoretical results.