A new tension B-spline method for third-order self-adjoint singularly perturbed boundary value problems

The aim of this paper is to present a new kind of tension B-spline, called hyperbolic-trigonometric tension B-spline of order n, which is generated over the space span {sin(τt),cos(τt),sinh(τt),cosh(τt),1,t,…,tn−5},n≥5, where τ is tension parameter. This kind of B-spline has most properties of usual polynomial B-splines and enjoys some other advantageous properties as well. Also, hyperbolic-trigonometric tension B-spline method is applied for solving self-adjoint singularly perturbed problems. We use some numerical examples to illustrate the accuracy and implementation of the method.