Order Singular Perturbation Problem Of The Difference Scheme

Consider the boundary value problemwhere e denotes the small parameter, s(x) is differentiable in [a,b], c(r) and f(x) are continuous in [a,b]. In this paper, we shall study the three-point form of the approximating problem (1.1):The difference scheme associated to problem (1.1) isIts matrix follows:Then the existence and uniqueness of the solution to the difference question is equivalent to the invertibility of T. From [4], the sufficientcondition of the latter is so do for the former.According to the sufficient condition of the well-conditional in T [4],we proved the same conclusion as and keep sign.Theorem 4.7 As the following conditions are satisfied, the matrix T is nonsingular and well-conditional.1) and keep signTheorem 4.8 As the following conditions are satisfied, the matrix T is nonsingular and well-conditional. 1) and keep signIn the discussing of the step size hi , we obtained Theorem 5 . 2 from the above theorem.Theorem 5. 2 In the expression of and , let hi = h, for all i, then T is nonsingular and if T is well-conditional.From theorem 5.2, if and , the condition number K( T)is independent from The result shows that in the construction ofthe difference scheme to (1.1), the number of the net points should be the same order of e -1.