General linear methods in the Nordsieck form have been introduced for the numerical solution of Volterra integral equations. In this paper, we introduce general linear methods of order p and stage order q = p for the numerical solution of Volterra integral equations in general form, rather than Nordsieck form. A-and V 0 (α)-stable methods are constructed and applied on stiff problems to show their efficiency.
General Linear Methods (GLMs) were introduced as the natural generalizations of the classical Runge-Kutta and linear multistep methods. An extension of GLMs, so-called SGLMs (GLM with second derivative), was introduced to the case in which second derivatives, as well as first derivatives, can be calculated. In this paper, we introduce the definitions of consistency, stability and convergence for an SGLM. It will be shown that in SGLMs, stability and consistency together are equivalent to convergence. Also, by introducing a subclass of SGLMs, we construct methods of this subclass up to the maximal order which possess Runge-Kutta stability property and A-stability for implicit ones.
Early repolarization syndrome (ERS), demonstrated as J-point elevation on an electrocardiograph, was formerly thought to be a benign entity, but the recent studies have demonstrated that it can be linked to a considerable risk of life - threatening arrhythmias and sudden cardiac death (SCD). Early repolarization characteristics associated with SCD include high - amplitude J-point elevation, horizontal and/or downslopping ST segments, and inferior and/or lateral leads location. The prevalence of ERS varies between 3% and 24%, depending on age, sex and J-point elevation (0.05 mV vs 0.1 mV) being the main determinants. ERS patients are sporadic and they are at a higher risk of having recurrent cardiac events. Implantable cardioverter-defibrillator implantation and isoproterenol are the suggested therapies in this set of patients. On the other hand, asymptomatic patients with ERS are common and have a better prognosis. The risk stratification in asymptomatic patients with ERS still remains a grey area. This review provides an outline of the up-to-date evidence associated with ERS and the risk of life - threatening arrhythmias. Further prospective studies are required to elucidate the mechanisms of ventricular arrhythmogenesis in patients with ERS.
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