一类双曲型方程的摄动有限差分格式及其数值研究.pdfVIP

Abstract This topic partially originates from Hunan Province education department block item of Professor Ming Jun Li In this paper, we use the perturbation finite difference (PFD) methods which were put forward by Z. Gao in 1990s to study a class of the hyperbolic conservation equation numerically. Approximately, it is carried on the Numerical and theoretical investigation of the hyperbolic equations’ difference. The first order hyperbolic conservation equation’s time first order backward difference and spatial first order upwind difference scheme was expanded to the time and spacial step-size’s power series by scale perturbation. The coefficients of the power series are determined by means of increasing precision of the scheme and maintaining high resolution rate. From this, we obtained a new scheme on time and spatial PFD scheme of the hyperbolic conservation equations, which was both two-order precisions and non-vibrates. The PFD scheme of the hyperbolic conservation equation preserves the first order upwind difference scheme’s simple structural style. It can achieve two-order precisions by using only three nodes of time and spacial respectively and avoid non-physical numerical vibration of the three-point two-order central difference scheme. In this paper, we show the stability conditions. Then, we make the numerical comparison with PFD two-order TVD scheme, we show that the new scheme is a high precision and high resolution rate scheme. Numerically, it powerfully support the perturbation finite difference (PFD) methods. Keywords: perturbation finite difference, hyperbolic equations, power series, stability II 湘潭大学 学位论文原创性声明 本人郑重声明：所呈交的论文是本人在导师的指导下独立进行研究所 取得的研究成果。除了文中特别加以标注引用的内容外，本论文不包含任 何其他个人或集