A. Abdollahi - Department of Mathematics, Maragheh Branch, Islamic Azad University, Maragheh, Iran.
E. Babolian - Department‎ of Mathematical Sciences and Computer, Kharazmi University, Tehran, ‎Iran‎.

In this article‎, ‎a new scheme inspired from collocation method is‎ ‎presented for numerical solution of stiff initial-value problems and Fredholm integral equations of the first kind based on the derivatives of residual function‎. ‎Then‎, ‎the error analysis‎ ‎of this method is investigated by presenting an error bound‎. ‎Numerical comparisons indicate that the‎ ‎presented method yields accurate approximations in many‎ ‎cases in which the collocation method is ‎failed.

Local annihilation method‎, ‎Residual function‎, ‎Stiff problems‎, ‎Ill-posed ‎problems