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. Manuscript profile