A collocation method with dierent types of B-spline functions such as trigonometric and exponential cubic B-splines
functions are proposed from many researchers for studying the numerical solutions of many physical nonlinear partial
dierential equations and ordinary dierential equations. In this paper, a collocation nite dierence scheme based on
trigonometric and exponential cubic B-splines functions are investigated and applied for the numerical solution of two-point
boundary value problems. The convergence of trigonometric and exponential cubic B-splines is proved using diagonally
dominant matrices. The numerical examples show that our method is very eective and the maximum absolute error is
acceptable.