Convergence results for implicit–explicit general linear methods

Sequential second derivative general linear methods for stiff systems

‎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 p...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Two Convergence Results for Continuous Descent Methods

We consider continuous descent methods for the minimization of convex functionals defined on general Banach space. We establish two convergence results for methods which are generated by regular vector fields. Since the complement of the set of regular vector fields is σ-porous, we conclude that our results apply to most vector fields in the sense of Baire’s categories.

Convergence results for linear multistep methods for quasi-singular perturbed problem systems

Stiff behavior occurs in a variety of ODE systems relevant in applications. The notion of stiffness is a phenomenological one, and a stability and error analysis of numerical methods has been based either on simple models or particular problem structures. In particular, stiff initial value problems in standard singular perturbation form are well understood. However, problems of this type exhibi...

sequential second derivative general linear methods for stiff systems

‎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 p...