對(duì)流方程各種格式代碼matlab

1、精選優(yōu)質(zhì)文檔-傾情為你奉上對(duì)流方程偏微分方程的數(shù)值解法用迎風(fēng)格式解對(duì)流方程function u = peYF(a,dt,n,minx,maxx,M)format long;h = (maxx-minx)/(n-1);if a>0    for j=1:(n+M)        u0(j) = IniU(minx+(j-M-1)*h);    endelse       for j=1:(n+M)

2、60;       u0(j) = IniU(minx+(j-1)*h);    endend   u1 = u0;for k=1:M    if a>0         for i=(k+1):n+M            u1(i) = -dt*a*

3、(u0(i)-u0(i-1)/h+u0(i);        end    else        for i=1:n+M-k            u1(i) = -dt*a*(u0(i+1)-u0(i)/h+u0(i);        end&#

4、160;   end    u0 = u1;endif a>0    u = u1(M+1):M+n);else    u = u1(1:n);endformat long;用拉克斯-弗里德里希斯格式解對(duì)流方程function u = peHypbLax(a,dt,n,minx,maxx,M)format long;h = (maxx-minx)/(n-1);for j=1:(n+2*M)        u0(

5、j) = IniU(minx+(j-M-1)*h);end u1 = u0;for k=1:M    for i=k+1:n+2*M-k        u1(i) = -dt*a*(u0(i+1)-u0(i-1)/h/2+(u0(i+1)+u0(i-1)/2;    end    u0 = u1;endu = u1(M+1):(M+n);format short;用拉克斯-溫德洛夫格式解對(duì)流方程function u = peL

6、axW(a,dt,n,minx,maxx,M)format long;h = (maxx-minx)/(n-1);for j=1:(n+2*M)        u0(j) = IniU(minx+(j-M-1)*h);end u1 = u0;for k=1:M    for i=k+1:n+2*M-k        u1(i) = dt*dt*a*a*(u0(i+1)-2*u0(i)+u0(i-1)/2/h/h -

7、.                   dt*a*(u0(i+1)-u0(i-1)/h/2+u0(i);    end    u0 = u1;endu = u1(M+1):(M+n);format short;用比姆-沃明格式解對(duì)流方程function u = peBW(a,dt,n,minx,maxx,M)format long;h = (maxx-min

8、x)/(n-1);for j=1:(n+2*M)        u0(j) = IniU(minx+(j-2*M-1)*h);end u1 = u0;for k=1:M    for i=2*k+1:n+2*M        u1(i) = u0(i)-dt*a*(u0(i)-u0(i-1)/h-a*dt*(1-a*dt/h)* .       &

9、#160;    (u0(i)-2*u0(i-1)+u0(i-2)/2/h;    end    u0 = u1;endu = u1(2*M+1):(2*M+n);format short;用Richtmyer多步格式解對(duì)流方程function u = peRich(a,dt,n,minx,maxx,M)format long;h = (maxx-minx)/(n-1);for j=1:(n+4*M)        u0(j) = In

10、iU(minx+(j-2*M-1)*h);end u1 = u0;for k=1:M    for i=2*k+1:n+4*M-2*k        tmpU1 = -dt*a*(u0(i+2)-u0(i)/h/4+(u0(i+2)+u0(i)/2;        tmpU2 = -dt*a*(u0(i)-u0(i-2)/h/4+(u0(i)+u0(i-2)/2;    

11、60;           u1(i) = -dt*a*(tmpU1-tmpU2)/h/2+u0(i);    end    u0 = u1;endu = u1(2*M+1):(2*M+n);format short;用拉克斯-溫德洛夫多步格式解對(duì)流方程function u = peMLW(a,dt,n,minx,maxx,M)format long;h = (maxx-minx)/(n-1);for j=1:(n+2*M) 

12、       u0(j) = IniU(minx+(j-M-1)*h);end u1 = u0;for k=1:M    for i=k+1:n+2*M-k        tmpU1 = -dt*a*(u0(i+1)-u0(i)/h/2+(u0(i+1)+u0(i)/2;        tmpU2 = -dt*a*(u0(i)-u0(i-1)/h/2+(u0

13、(i)+u0(i-1)/2;                u1(i) = -dt*a*(tmpU1-tmpU2)/h+u0(i);    end    u0 = u1;endu = u1(M+1):(M+n);format short;用MacCormack多步格式解對(duì)流方程function u = peMC(a,dt,n,minx,maxx,M)format long;h = (ma

14、xx-minx)/(n-1);for j=1:(n+2*M)    u0(j) = IniU(minx+(j-M-1)*h);end u1 = u0;for k=1:M    for i=k+1:n+2*M-k        tmpU1 = -dt*a*(u0(i+1)-u0(i)/h+u0(i);        tmpU2 = -dt*a*(u0(i)-u0(i-1)/h+u0(i-1

15、);                u1(i) = -dt*a*(tmpU1-tmpU2)/h/2+(u0(i)+tmpU1)/2;    end    u0 = u1;endu = u1(M+1):(M+n);format short;用拉克斯-弗里德里希斯格式解二維對(duì)流方程的初值問(wèn)題function u = pe2LF(a,b,dt,nx,minx,maxx,ny,miny,maxy

16、,M)%啦-佛format long;hx = (maxx-minx)/(nx-1);hy = (maxy-miny)/(ny-1);for i=1:nx+2*M    for j=1:(ny+2*M)        u0(i,j) = Ini2U(minx+(i-M-1)*hx,miny+(j-M-1)*hy);    endend u1 = u0;for k=1:M    for i=k+1:nx+2*M-k &

17、#160;      for j=k+1:ny+2*M-k            u1(i,j) = (u0(i+1,j)+u0(i-1,j)+u0(i,j+1)+u0(i,j-1)/4 .                 -a*dt*(u0(i+1,j)-u0(i-1,j)/2

18、/hx .                 -b*dt*(u0(i,j+1)-u0(i,j-1)/2/hy;        end    end    u0 = u1;endu = u1(M+1):(M+nx),(M+1):(M+ny);format short;    

19、;        用拉克斯-弗里德里希斯格式解二維對(duì)流方程的初值問(wèn)題function u = pe2FL(a,b,dt,nx,minx,maxx,ny,miny,maxy,M)%近似分裂format long;hx = (maxx-minx)/(nx-1);hy = (maxy-miny)/(ny-1);for i=1:nx+4*M    for j=1:(ny+4*M)        u0(i,j) = Ini2U

20、(minx+(i-2*M-1)*hx,miny+(j-2*M-1)*hy);    endend u1 = u0;for k=1:M    for i=2*k+1:nx+4*M-2*k        for j=2*k-1:ny+4*M-2*k+2            tmpU(i,j) = u0(i,j) - a*dt*(u0(i+1,j)-u0(i-1,j)/2/hx + .                (a*