Long time integration of large Stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region. In this paper, we apply second derivative general linear methods to solve some Stiff chemical problems such as chemical Akzo Nobel problem, HIRES problem and OREGO problem.

In this paper, the modified matrix exponential (MME) method under zero-order hold (ZOH) assumption, is applied to solve systems of Stiff ordinary differential equations. Some examples are given to illustrate the accuracy and effectiveness of the method. We compare our results with results obtained by matrix exponential (ME) method and by the Matlab ode23 solver.

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, 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.