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12: Paper Source PDF document

Paper's Title:

Approximation of Derivatives in a Singularly Perturbed Second Order Ordinary Differential Equation with Discontinuous Terms Arising in Chemical Reactor Theory


R. Mythili Priyadharshini and N. Ramanujam

Department of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, India.


In this paper, a singularly perturbed second order ordinary differential equation with a discontinuous convection coefficient arising in chemical reactor theory is considered. A robust-layer-resolving numerical method is suggested. An ε-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

2: Paper Source PDF document

Paper's Title:

A Nonlinear Proximal Alternating Directions Method for Structured Variational Inequalities


M. Li

Department of Management Science and Engineering, School of Economics and Management
Southeast University, Nanjing, 210096,


In this paper, we present a nonlinear proximal alternating directions method (NPADM) for solving a class of structured variational inequalities (SVI). By choosing suitable Bregman functions, we generalize the proximal alternating directions method proposed by He, et al.. The convergence of the method is proved under quite mild assumptions and flexible parameter conditions.

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