Sextic spline solution of a singularly perturbed boundary-value problems

A sixth-order uniform mesh difference scheme using sextic splines for solving a self-adjoint singularly perturbed two-point boundary-value problem arising in the study of chemical reactor theory, of the form-εu″+p(x)u=f(x),p(x)>0,u(0)=αo,u(1)=α1is derived. Our scheme leads to a pentadiagonal linear system. The convergence analysis is given and the method is shown to have fifth-order convergence. Numerical illustrations are given to confirm the theoretical analysis of our method.