We present greedy unsymmetric collocation schemes for solving linear elliptic partial differential equations using radial basis functions. The proposed approach circumvents the ill-conditioning problem associated with the standard collocation technique and enables the efficient solution of problems requiring a large set of collocation points. Numerical studies indicate that the accuracy of gree...

Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of “blow-up collocation solution” and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we d...

 In view of the fact that pre-service teachers’ critical reflection through evaluating teaching activity of their peers is an important part of practicum activity, the current study aimed to analyze the recall and reflection journals written by pre-service teachers to identify and evaluate the discoursal features of their journals. To this end, a total of 272 recall and reflection journals writ...

This study aimed to investigate the effect of pre-teaching new vocabulary items via audio-visuals on Iranian EFL learners’ reading comprehension ability. The question this study tried to answer is if pre-teaching new vocabulary items via audio-visuals have any effect on Iranian EFL learners’ reading comprehension ability. To find the answer to the question, 30 intermediate level stu...

PURPOSE Although the importance of bedside teaching is generally recognized, there is no published report on the actual experience or effects of bedside teaching in Korea. We aimed to study the effects and share the experience of bedside teaching during a clerkship in pulmonary medicine. METHODS Bedside teaching was administered to 120 students through Year 3. To evaluate the improvement in c...

The purpose of this research was to investigate the effect of practice teaching in Second Life on the change of preservice teachers’ teaching efficacy, and the difference of changes between individual teaching practice and collaborative teaching practice in their teaching efficacy. Participants were placed into the individual teaching practice or collaborative teaching practice group as a part ...

Abstract. A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the...