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1、。对下面的一阶对流扩散方程?u+a?u=0x∈(-∞,∞),t>0?t?tu(x,0)=U(x)x∈(-∞,∞)(1.1)对求解区间[0,1]10x+1-0.1≤x≤0U(x)=-10x+10≤x≤0.10其余Matlab程序functionu=yingfeng(a,dt,n,minx,maxx,M)%方程中的常数：a%时间步长：dt%空间节点个数：n%求解区间的左端：minx%求解区间的右端：naxx%时间步的个数：M%求解区间上的数值解：uformatlong;h=(maxx-minx)/(n-1);ifa>0forj=1
2、:(n+M)u0(j)=IniU(minx+(j-M-1)*h);endelseforj=1:(n+M)u0(j)=IniU(minx+(j-1)*h);endendu1=u0;fork=1:Mifa>0fori=(k+1):n+Mu1(i)=-dt*a*(u0(i)-u0(i-1))/h+u0(i);-可编辑修改-。endelsefori=1:n+M-ku1(i)=-dt*a*(u0(i+1)-u0(i))/h+u0(i);endendu0=u1;endifa>0u=u1((M+1):M+n);elseu=u1(1:n);e
3、ndformatlong;functionux=IniU(x)formatlong;ifx<=0ifx>=-0.1ux=10*(x+0.1);elseux=0;endelseifx<=0.1ux=-10*(x-0.1);elseux=0;endendend在保持其他量不变的情况下，通过改变dt的值来改变来分析时间步长dt和空间步长h的取值关系r=ΔtΔtat=aar=a=事实上令h则有h(maxx-minx)/(n-1)u=yingfeng(1,0.00001,101,0,1,100);t(n-1);-可编辑修改-。plot
4、(u)u=yingfeng(1,0.001,101,0,1,100);plot(u)u=yingfeng(1,0.003,101,0,1,100);>>plot(u)u=yingfeng(1,0.005,101,0,1,100);plot(-可编辑修改-。u)u=yingfeng(1,0.006,101,0,1,100);plot(u)u=yingfeng(1,0.007,101,0,1,100);plot(u)u=yingfeng(1,0.008,101,0,1,100);-可编辑修改-。plot(u)u=yingfeng(
5、1,0.009,101,0,1,100);plot(u)u=yingfeng(1,0.01,101,0,1,100);plot(u)u=yingfeng(1,0.011,101,0,1,100);plot(-可编辑修改-。u)u=yingfeng(1,0.012,101,0,1,100);plot(u)u=yingfeng(1,0.013,101,0,1,100);plot(u)>>u=yingfeng(1,0.014,101,0,1,100);>>-可编辑修改-。plot(u)>>u=yingfeng(1,0.017,101
6、,0,1,100);>>plot(u)>>u=yingfeng(1,0.020,101,0,1,100);>>plot(u)u=yingfeng(1,1,101,0,1,100);plot(-可编辑修改-。u)由以上得到的图像我们可以知道当ar≤1，既Δt≤1ha时波是稳定的，且随着时间的增长向右传播；ar>1时，波开始不稳定，且向左不断的扩散。ar=1或t→0-可编辑修改-。THANKS!!!致力为企业和个人提供合同协议，策划案计划书，学习课件等等打造全网一站式需求欢迎您的下载，资料仅供参考-可编辑修改-
