H方程式的一些加速收斂方法

Abstract

本篇論文主要是討論H方程式的遞迴數值解.我們將此方程式改寫成兩種型 式,並限制其中兩個參數(c與.alpha.)的條件.首先,我們設法去求得此兩 種收斂方法的譜半徑;其次,引進加速收斂的概念,去改善在(c=1)的奇異點 情況;最後,再輔以數值解去驗證我們理論的精確性與否. In this paper, some acceleration techniques are applied to numerical solutions of the discretized H-equations. Such equation is formulated as two well-known fixed point of the types. Here c denotes the fraction of scattering per collision and is assumed to be conserative. We first show that the spectral radii of the Jacobi matrix. We next propose some simple ideas to accelerate the convergence of one point iteration. The numerical results gives very significant improvements when our method apply to both fprmulations.