Chebyshev approximations for a boundary value problem of differential difference equations

✍ Scribed by Mitusunou Kurihara; Tomohiro Suzuki

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 333 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00503-x

✦ Synopsis

A boudary value problem is studied for a system of nonlinear differential difference equations of retarded types. We investigate an existence theorem of solutions, a method of approximation and an error estimation and can prove two main theorems. The first theorem says that one can assure the existence of an exact solution with isolated conditions by checking several assumptions on an obtained approximate solution and gives a method to have an error bound for the obtained approximate solution. The second theorem says that for any solution with isolated conditions there exists an approximate solution accurately as it is desired by computing the finite series of Chebyshev polynomials.