Parametric cubic spline solution of two point boundary value problems Arshad Khan Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202-002, India Abstract In this paper, we use parametric cubic spline function to develop a numerical method, which is fourth order for a specific choice of the parameter, for computing smooth ap- proximations to the solution for second order boundary value problems. Some numerical evidence is also included to demonstrate the superiority of our method. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Parametric cubic spline function; Finite difference method; Boundary value problems; NumerovÕs method 1. Introduction We consider the two-point boundary value problem y 00 ðxÞ¼ f ðxÞy ðxÞþ gðxÞ; a 6 x 6 b; y ðaÞ¼ a 0 ; y ðbÞ¼ a 1 ; ð1:1Þ where f ðxÞ and gðxÞ are continuous functions on ½a; b and a; b; a 0 ; a 1 are ar- bitrary real finite constants. Such problems arise in the theory which describes the deflection of plates and a number of other scientific applications. In general it is difficult to obtain the analytical solution of (1.1) for arbitrary choices of f ðxÞ and gðxÞ. We usually employ some numerical method for obtaining an approximate solution of the problem (1.1). The standard numerical methods E-mail addresses: akhan@bharatmail.com, akhan1234in@yahoo.co.in (A. Khan). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(03)00701-X Applied Mathematics and Computation 154 (2004) 175–182 www.elsevier.com/locate/amc