An optimal uniformly convergent oci difference scheme for a singular perturbation problem^∗

^∗This research was supported partly by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grant JF 799)

Abstract

The exponentially fitted tridiagonal OCI difference scheme for singularly perturbed problem is derived. The error at the grid points is bounded by , is a constant independent of ∊ and h, h is the step of a uniform mesh. The scheme has the maximal order of the classical and the uniform accuracy.

Keywords:

• Singular perturbation
• small parameter
• uniform convergency
• spline difference schemes
• numerical solution for differential equations

C.R. Categories:

• G1.7

AMS Subject classifications:

• 65L10

^∗This research was supported partly by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grant JF 799)

^∗This research was supported partly by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grant JF 799)

Notes

^∗This research was supported partly by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grant JF 799)