Generalized Picard iterations: A class of iterated Runge–Kutta methods for stiff problems

A generalized implicit enumeration algorithm for a class of integer nonlinear programming problems

Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...

New Perturbed Iterations for a Generalized Class of Strongly Nonlinear Operator Inclusion Problems in Banach Spaces

The purpose of this paper is to introduce and study a new kind of generalized strongly nonlinear operator inclusion problems involving generalized m-accretive mapping in Banach spaces. By using the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang, we also prove the existence theorem of the solution for this kind of operator inclusion problems and construct ...

Error Analysis for Picard-Chebyshev Iterations

A class of explicit one-step methods of order two for stiff problems

In this paper we introduce a new class of explicit one-step methods of order 2 that can be used for solving stiff problems. This class constitutes a generalization of the two-stage explicit Runge-Kutta methods, with the property of having an A-stability region that varies during the integration in accordance with the accuracy requirements. Some numerical experiments on classical stiff problems ...

An improved class of generalized Runge-Kutta methods for stiff problems. Part II: The separated system case