A Review of Time Discretization of Semi-linear Parabolic Problems

Zainal Abdul Aziz ； Nazeeruddin Yaacob ； Mohammadreza AskaripourLahiji ； Mahdi Ghanbari

《Research Journal of Applied Sciences, Engineering and Technology》 4卷19期 (2012/10) Pp. 3539-3543

並列摘要

In this study, exponentialRunge-Kutta methods of collocation type are considered for linear and semi-linear parabolic problems. An abstract Banach space framework of sectorial operators and Lipchitz continuous nonlinearities are selected for the analysis. Exponential Runge-Kutta methods of collocation type are also employed for parabolic Cauchy problems. Moreover, numerical experiments have been presented for illustration of parabolic problems.

並列關鍵字

Exponential integrators ； exponential quadrature rules ； Range-kutta methods ； schrödinger equation ； semi-linear parabolic problems