The ordinary successive approximations method and Padé approximants for solving a differential equation with variant retarded argument
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.
differential equations with retarded arguments
scientific article; zbMATH DE number 1961566