Series solution of nonlinear two-point singularly perturbed boundary layer problems

✍ Scribed by M. Turkyilmazoglu

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 303 KB
• Volume: 60
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2010.07.052

✦ Synopsis

method Absolute residual error a b s t r a c t

The present paper is concerned with the approximate analytic series solution of the nonlinear two-point second-order singularly perturbed boundary value problems. In place of the traditional numerical, perturbation or asymptotic methods, a homotopy technique is employed. It is shown that proper choices of an auxiliary linear operator and also an initial approximation during the implementation of the homotopy analysis method (HAM) can yield uniformly valid and accurate solutions. The fast convergence of the method is ensured by the optimal convergence control parameter obtained through the absolute residual error concept. To demonstrate the favor of the HAM over the traditional finitedifference techniques several nonlinear problems have been solved and compared.