偏微分差分四种格式的matlab程序.doc

偏微分差分四种格式的matlab程序（1）Lax-Fridrichs格式function u = LaxFridrichs(a,dt,n,x1,x2,m)format long;h = (x2-x1)/(n-1);for j=1:(n+2*m) u0(j) =U(x1+(j-m-1)*h);end u1 = u0;for k=1:m for i=k+1:n+2*m-k u1(i) = -(dt/h)*a*(u0(i+1)-u0(i-1)/2+(u0(i+1)+u0(i-1)/2; end u0 = u1;endx=0.01:0.01:n/100; u = u1(m+1):(m+n);plot(x,u,r); axis(0 1 -0.5 1.5);hold ony=1.*(x0.5);plot(x,y,c)title(Lax-Fridrichs)format short;function ux =U(x) format long; if x u = LaxFridrichs(1,0.005,101,0,1,100) 运行结果（2）迎风格式function u = Yingfeng(a,dt,n,x1,x2,m)format long;h = (x2-x1)/(n-1);if a0 for j=1:(n+m) u0(j) =U(x1+(j-m-1)*h); endelse for j=1:(n+m) u0(j) =U(x1+(j-1)*h); endend u1 = u0;for k=1:m if a0 for i=(k+1):n+m u1(i) = u0(i)-(dt/h)*a*(u0(i)-u0(i-1); end else for i=1:n+m-k u1(i) = u0(i)-(dt/h)*a*(u0(i+1)-u0(i); end end u0 = u1;endx=0.01:0.01:n/100; u = u1(m+1):(m+n);plot(x,u,r);axis(0 1 -0.5 1.5);hold ony=1.*(x0.5);plot(x,y,c)format short;title(迎风格式)function ux =U(x) format long; if x u=Yingfeng(1,0.005,101,0,1,100) 运行结果（3）Lax-Wendroff格式function u = LaxWendroff(a,dt,n,x1,x2,m)format long;h = (x2-x1)/(n-1);for j=1:(n+2*m) u0(j) =U(x1+(j-m-1)*h);end u1 = u0;for k=1:m for i=k+1:n+2*m-k u1(i) = u0(i)-(dt/h)*a*(u0(i+1)-u0(i-1)/2+(dt/h)2*a*a*(u0(i+1)-2*u0(i)+u0(i-1)/2; end u0 = u1;endx=0.01:0.01:n/100; u = u1(m+1):(m+n);plot(x,u,r); axis(0 1 -0.5 1.5);hold ony=1.*(x0.5);plot(x,y,c)title(Lax-Wendroff)format short function ux =U(x) format long; if x u= LaxWendroff(1,0.005,101,0,1,100) 运行结果（4）Beam-Warming格式function u =BeamWarming(a,dt,n,x1,x2,m)format long;h = (x2-x1)/(n-1);for j=1:(n+2*m) u0(j) =U(x1+(j-m-1)*h);end u1 = u0; for k=1:m for i=k+2:n+2*m-k u1(i) = u0(i)-a*(dt/h)*(u0(i)-u0(i-1)-a*(dt/h)*(1-a*(dt/h)*(u0(i)-2*u0(i-1)+u0(i-2)/2; end u0 = u1;endx=0.01:0.01:n/100; u = u1(m+1):(m+n);plot(x,u,r); axis(0 1 -0.5 1.5);hold ony=1.*(x0.5);plot(x,y,c)title(Beam-