标题：Finite difference fractional step methods for the transient behavior of a semiconductor device
作者机构：[Yuan Yirang] Institute of Mathematics, Shandong University, Jinan, ShanDong 250100, China.
通讯作者地址：[Yuang, YR]Shandong Univ, Inst Math, Jinan 250100, Peoples R China.
关键词：General region semiconductor device;3-dimensional heat conduction;characteristic finite difference;parallel fractional steps;l2 error estimate
摘要：Characteristic finite difference fractional step schemes are put forward. The electric Potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.