Chebyshev approximations for a boundary value problem of differential difference equations

A boudary value problem is studied for a system of nonlinear differential d ifference equations of retarded types. We investigate an existence theorem of solutions, a method of approximation and an error estimation and can pro ve two main theorems. The first theorem says that one can assure the existe nce of an exact solution with isolated conditions by checking several assum ptions on an obtained approximate solution and gives a method to have an er ror bound for the obtained approximate solution. The second theorem says th at fo any solution with isolated conditions there exists an approximate sol ution accurately as it is desired by computing the finite series of Chebysh ev polynomials.