Abstract.

We consider the self-adjoint singularly perturbed two-point boundary value prob-lems. We know that the numerical methods for solution of such problems based on non-polynomial spline in grid points, can produce the fourth order method only. So that we lookfor an alternative to obtain higher order methods. We develop the non-polynomial spline inoff-step points to rise the order of accuracy. Based on such spline, the purposed new methodsare fourth, sixth and eighth-order accurate.

Keywords:

Self-adjoint singularly-perturbed boundary value problem, Non-polynomial spline,Convergence analysis, Numerical conclusion.