Local Annihilation Method and Some Stiff Problems

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. The efficiency of the new method is compared with the efficiency of the collocation method by presenting some stiff and ill-posed test problems. Numerical comparisons indicate that the presented method yields accurate approximations in many cases in which the collocation method is failed.