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jiasen1980

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%FWT on the NLS equation i*du/dt+alpha*d^2u/dx^2+nu*|u|^2*u=0
%x=linspace(-3,3,1000);u=exp(2*x.^2);[c,L]=wavedec(u,3,'sym6');A=wrcoef('a',c,L,'sym6',3);
%plot(x,u,'x',x,A,'r')
%-----Claculate the wavelet-------
xmax=16;
level=3;
alpha=1/2;
nu=1;
deltat=5*10^(-5);
maxtime=2;
iter=3;
wav='sym6';
[phi,psi,xval]=wavefun(wav,iter);
hval=xval(2)-xval(1);
MX=max(xval);
s=1;
% mm=0;
% jump=10^(s+1);
flag=1;
for t=0:deltat:maxtime
if flag==1
flag=0;
thresh=2^(level-3)*10^-5;
phin=2^(level/2)*phi;
psin=2^(level/2)*psi;
lenphi=length(phin);
shift=floor(lenphi/MX);
N=xmax*2^level-(MX-1);
lenPHI=(N-1)*shift+lenphi;
x=linspace(-xmax/2,xmax/2,lenPHI);
h=x(2)-x(1);
%--------------Clculate the initial approximation of u--------------
if t==0
ua=3*sech(x);
end
t=0;
for L=1:N
aold(1,L)=h*ua((L-1)*shift+1L-1)*shift+lenphi)*phin';
end
for L=1:N
b(1,L)=h*ua((L-1)*shift+1L-1)*shift+lenphi)*psin';
end
u0=zeros(1,lenPHI);
for L=1:N
u0(1,(L-1)*shift+1L-1)*shift+lenphi)=u0(1,(L-1)*shift+1L-1)*shift+lenphi)+aold(1,L)*phin;
end
figure
plot(x,ua,'k',x,u0,'r');
title(strcat('xmax=',num2str(xmax),',alpha=',num2str(alpha),',\nu=',num2str(nu),',maxtime=',num2str(maxtime),',deltat=',num2str(deltat),',level=',num2str(level),',iter=',num2str(iter),',time=',num2str(t)));
%----Calculate KM Matrix for sym6
load sym6KMburg3;
for L=1:N
for K=1:N
if abs(L-K) KM(L,K)=sym6KMburg3(K-L+MX)*2^(2*level);
end
end
end
%-------------
load sym6LambdaNLS3;
end
% U=zeros(floor(maxtime/(jump*deltat))+1,lenPHI);
%----Calculate C Matrix-----------------
C=zeros(N,N);
for L=1:N
for K=1:N
if abs(L-K) for m =1:N
if abs(m-K) for n=1:N
if abs(n-K) C(L,K)=C(L,K)+aold(1,n)*2^(level)*sym6LambdaNLS3(KL+MX,m-L+MX,n-L+MX)*conj(aold(1,m));
end
end
end
end
end
end
end
% % for L=1:N
% % for K=1:N
% % if abs(L-K) % % Mat(L,K)=deltat*(nu*C(L,K)+alpha*sym6KMburg3(KL+MX)*2^(2*level));
% % end
% % end
% % end
% %a=a+i*a*Mat;
anon=aold+i*deltat*aold*nu*C;
alin=anon+i*deltat*anon*alpha*KM;
anew=alin;
aold=anew;
if max(abs(aold))>50
u=zeros(1,lenPHI);
for L=1:N
u(1,(L-1)*shift+1L-1)*shift+lenphi)=u(1,(L-1)*shift+1L-1)*shift+lenphi)+abs(aold(1,L))*phi;
end
figure
plot(x,u0,'r',x,u,'k');
title(strcat('xmax=',num2str(xmax),',alpha=',num2str(alpha),',\nu=',num2str(nu),',maxtime=',num2str(maxtime),',deltat=',num2str(deltat),',level=',num2str(level),',iter=',num2str(iter),',time=',num2str(t)));
break;
end
u=zeros(1,lenPHI);
for L=1:N
u(1,(L-1)*shift+1L-1)*shift+lenphi)=u(1,(L-1)*shift+1L-1)*shift+lenphi)+abs(aold(1,L))*phin;
end
for L=1:N
b(1,L)=h*u((L-1)*shift+1L-1)*shift+lenphi)*psin';
end
if max(abs(b))>thresh
max(abs(b));
level=level+1;
flag=1;
ut=interp(u,2);
ua=ut(1:length(ut)-1);
% a=interp(a,2);
end
% if t == (mm*jump*deltat)
% u=zeros(1,lenPHI);
% for L=1:N
% u(1,(L-1)*shift+1L-1)*shift+lenphi)=u(1,(L-1)*shift+1L-1)*shift+lenphi)+abs(aold(1,L))*phin;
% end
% mm=mm+1;
% U(mm,=u;
% end
if t==deltat*10^(s+1)|t==deltat*10^(s+2)|t==deltat*10^(s+3)|t==deltat*10^(s+4)|t==0.5|t==0.75|t==1.5|t==1.75|t==2u=zeros(1,lenPHI);
for L=1:N
u(1,(L-1)*shift+1L-1)*shift+lenphi)=u(1,(L-1)*shift+1L-1)*shift+lenphi)+abs(aold(1,L))*phin;
end
figure
plot(x,u0,'r',x,u,'k');
title(strcat('xmax=',num2str(xmax),',alpha=',num2str(alpha),',\nu=',num2str(nu),',maxtime=',num2str(maxtime),',deltat=',num2str(deltat),',level=',num2str(level),',iter=',num2str(iter),',time=',num2str(t)));
end
end
% figure
% S=size(U);
% % tp=[0:1:S(1)-1];
% tp=linspace(0,maxtime,S(1));
% [X,T]=meshgrid(x,tp);
% mesh(X,T,U);
%
title(strcat('xmax=',num2str(xmax),',alpha=',num2str(alpha),',\nu=',num2str(nu),',maxtime=',num2str(maxtime),',deltat=',num2str(deltat),',level=',num2str(level),',iter=',num2str(iter),',time=',num2str(t)));
??? Error using ==> load
Unable to read file sym6KMburg3: No such file or directory.
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jiasen1980(½ð±Ò+2): 2010-09-09 14:12:28
ctgu_zheng(½ð±Ò+1):ÐÁ¿àÁË£¬¹ÄÀøÓ¦Öú¡£¡£¡£ 2010-09-09 16:59:36
jiasen1980(½ð±Ò+3): 2010-09-12 17:45:06
ÒýÓûØÌû:
Originally posted by jiasen1980 at 2010-09-08 17:23:33:
%FWT on the NLS equation i*du/dt+alpha*d^2u/dx^2+nu*|u|^2*u=0
%x=linspace(-3,3,1000);u=exp(2*x.^2);[c,L]=wavedec(u,3,'sym6');A=wrcoef('a',c,L,'sym6',3);
%plot(x,u,'x',x,A,'r')
%-----Claculate th ...

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