In this article, a new scheme inspired from collocation method is presented for numerical solution of sti initial-value problems and Fredholm integral equations of the  rst kind based on the derivatives of residual function. Then, the error analysis of this method is investigated by presenting an error bound. The effciency of the new method is compared with the effciency 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.

In this paper we present two classes of third derivative multi-step methods (TDMMs) that have good stability properties. Stability analysis of these methods is examined and our numerical results are compared with the results of the existing method.

After offering an overview of some of the main themes of Popper’s political thought, the paper argues that his account faces two problems relating to institutions. The first is that while Popper stresses the ‘rational unity of mankind’, and the potential for any of us to furnish criticisms of public policy, it is not clear what institutional means currently exist for this to enable this to take place. Second, Popper has stressed the conjectural character of even our best theories. However, at any point, some theories will have fared better in the face of criticism than others, and they may give us important information about constraints on our actions. At the same time, as ordinary citizens we may not be in a good position to understand the theories in question, let alone appraise the state of the specialised discussion of them. There is, it is suggested, a case for thinking of ways to institutionally entrench such fallible theories, especially in the current setting in which social media play an important role

In this paper, an efficient symbolic-numerical procedure based on the power series method is presented for solving a system of differential equations. The basic idea is to substitute power series into the differential equations and to find a polynomial system of coefficients, where a powerful symbolic computation technique (i. e., Grobner basis) is used to solve the system. In fact, the proposed method is an excellent bridge between symbolic and numeric computation and specially, enables us to find the solution of linear and non-linear Stiff systems. Numerical experiments were performed to justify our new approach.

Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs.The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge-Kutta stability conditions. In this paper, we introduce a technique for construction of an special case of SGLMs which decreases the complexity of finding coefficients matrices.

Stiff man syndrome is a rare disease characterized by painful chronic spasms in the muscle and skeletal system. This syndrome is an autoimmune neurologic disorder which is associated with thymoma. We treated a 32-year-old male patient with a type C thymoma (based on the World Health Organization classification) who had Stiff man syndrome. The patient underwent an extended thymectomy which brought about alleviation of his symptoms.