【摘要】 本文通过Mondelbrot数集映象变换式,讨论了Riccati常微分方程的数值解是如何与其变换式相对应,并由此与非线性常微分方程相联系的,提出M-Euler数学模型和算法。非线性过程常见于机械、电气和力学中。研究表明,这类非线性常微分方程的数值解的复变換式与M-数集有密切关系,它们具有分数维性质。本文研究了此类问题的理论、算法,并在计算机上输出可视性图象。更多还原

【Abstract】 In this paper, we discuss the fractal images of M-set and design its aigorithms. The programs are written in Ms-C language. Several illustrative images are included . It is generated on the GW-386,286 at HUST and NCC.Further more, in order to develop the application of fiactal geometry, we have studied tne M-Euler algorithrn and ussd it to simulate the non-linear systems such as Riccati otdinary non-linear differential equa tion, which can be used to visualize ths Duffing and Van dd Pol non-linear vibration systems.This work is supported by NSFC(No. 6883019) and CAD Lab. of Institute of Computing Technology, Academia Sinica.更多还原