Stochastic numerical analysis of nmlinear diffusion phenam

在研究计划的三年时间里，我们通过组织一些国际或国内的研讨会，以及参加期刊或会议论文集的方式，获得了各种重大研究成果，并展示了活动。(A)研究数学、物理或数学金融中一些重要的非线性现象的SDE或SPDE模型。(B)构造非线性扩散方程的随机解，如广义Burgers型方程、多孔介质方程等。(C)数值试验的非线性问题的数值逼近格式的研究2)Worksyop和会议的组织列表(A)京都大学RIMS第四届(1999年)和第五届(2001年)随机数字工作组的组织。(B)2001年8月在汉城举行的第53届三军情报局会议上组织受邀的论文会议(C)2001年9月在保加利亚瓦尔纳举行的关于MC和QMC会议的第二次iMACS会议上组织受邀的论文会议(D)在20013月在萨尔茨堡举行的关于MC和QMC会议的第三届iMACS会议上组织受邀的论文会议)最新文章的出版清单附在下一页。

Durring the three years period of the research plan, we have got various significant research results on the subjects and exhibited the activity by organizing some Workshops, International or domestic, and also by attending journals or of proceedings of the conferences.Here are the principal research ressults and the activities :1) Main results obtained through the research plan. (a) Studies on the SDE or SPDE models of some important nonlinear phenomea in math physics or math finances. (b) Construction of stochastic solutions of the nonlinear diffusion equations, such as the generalized Burgers eqaution, the equations of Porous medium. (c) Studies of the nunerical approximation schemes of those nonlinear problems with numrical experiments.2) List of organization of Worksyops and Sessions (a) Organization of the 4th (in 1999) and 5th (in 2001) Worksyop on stochastic numerics at RIMS of Kyoto University. (b) Organization of the invited paper session at the 53rd Meeting of ISI in Seoul, in August 2001 (c) Organization of the invited paper session at the 2nd IMACS Conference on MC ＆ QMC conference in Varna Bulgaria, in Septemper 2001 (d) Organization of the invited paper session at the 3rd IMACS Conference on MC ＆ QMC conference in Salzburg, in September 20013) Publication list of the very recent articles is attached in the next page.