A numerical implementation of the decomposition method for the Lienard equation Dog ˇan Kaya a , Salah M. El-Sayed b, * a Department of Mathematics, Firat University, Elazig 23119, Turkey b Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt Abstract In this study, a kind of explicit exact and numerical solutions to the Lienard equation is obtained, and the applications of the results to this equation has been compared with their known theoretical solution. This paper is particularly concerned with the Adomian decomposition method and the numerical results demonstrate that the new method is relatively accurate and easily implemented. Ó 2005 Elsevier Inc. All rights reserved. Keywords: The Adomian decomposition method; Numerical solutions; The Lienard equation 1. Introduction In this work, we consider the Lienard equation x 00 þ f ðxÞx 0 þ gðxÞ¼ eðtÞ; ð1Þ 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.01.104 * Corresponding author. Address: Department of Mathematics, Scientific Departments, Educa- tion College for Girls, Al-Montazah, Buraydah, Al-Qassim, Kingdom of Saudi Arabia. E-mail addresses: dkaya@firat.edu.tr (D. Kaya), ms4elsayed@yahoo.com (S.M. El-Sayed). Applied Mathematics and Computation 171 (2005) 1095–1103 www.elsevier.com/locate/amc