Uniform difference method for a parameterized singular perturbation problem G.M. Amiraliyev a, * , Mustafa Kudu b , Hakki Duru a a Yu ¨zu ¨ ncu ¨ Yıl University, Faculty of Art and Sciences, Department of Mathematics, 65080 Van, Turkey b Dicle University, Faculty of Education, Department of Mathematics, 56100 Siirt, Turkey Abstract We consider a uniform finite difference method on a B-mesh is applied to solve a sin- gularly perturbed quasilinear boundary value problem (BVP) depending on a para- meter. We give a uniform first-order error estimates in a discrete maximum norm. Numerical results are presented that demonstrate the sharpness of our theoretical analysis. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Parameterized problem; Singular perturbation; Uniform convergence; Finite difference scheme; B-mesh 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.07.068 * Corresponding author. E-mail addresses: gamirali2000@yahoo.com (G.M. Amiraliyev), hakkiduru2002@yahoo.com (H. Duru). Applied Mathematics and Computation 175 (2006) 89–100 www.elsevier.com/locate/amc