|
以下是一段解偏微分方程组的程序,谁能告诉我用的是什么方法解的,我怎么查了好多资料都看不出来啊,谢谢大家了! ( W9 q$ D6 J3 j4 ~1 G
, d0 S1 B: V! t6 g! s& o% % Programme pour leopard % . [8 L. h; o6 \! B& }" ^+ e
global d K F N - A% x: k1 E: h/ ^' d
N = 64 ) |7 ]/ A- p% b, V3 h: w6 A, V. T
dx = 1/N;
4 l( f8 r. m5 I$ q. n7 qd=10 K=0.01 F=0.1
3 Y c( S U2 o) Q dt=0.001;
( y% K7 d9 _, t' f: e3 CU=rand(N); V=rand(N);
) q( g+ d4 f& a H' iFourU=fft2(U); FourV=fft2(V); $ y+ \2 [' s' A# Y
for i=1:N, for j=1:N, i0=i-1; j0=j-1; if i0 > N/2 i0=1+N-i; end if j0 > N/2 j0=1+N-j; end FourU(i,j)=FourU(i,j)/(1+(i0*i0+j0*j0)/8); FourV(i,j)=FourV(i,j)/(1+(i0*i0+j0*j0)/8); end end
+ f# Q- d3 Z+ @" `3 Z' S) n$ |% dU=real(ifft2(FourU)); V=real(ifft2(FourV));
1 l% l' v+ s/ G# {compteur=0; " o8 [+ ~( o2 d7 ^- T* h+ q' |
for t=0:dt:1, . ?% r( ~" ^; B+ F7 E3 [9 z1 G; n
format long max(max(U)) max(max(V)) min(min(V)) & n6 i- A( R1 X" W* J. A
FourU=fft2(U); FourV=fft2(V); ! v' m- A% M# h5 [; c7 z
for i=1:N, for j=1:N, i0=i-1; j0=j-1; if i0 > N/2 i0=1+N-i; end if j0 > N/2 j0=1+N-j; end FourU(i,j)=FourU(i,j)*exp(-dt*(i0*i0+j0*j0)/10); FourV(i,j)=FourV(i,j)*exp(-d*dt*(i0*i0+j0*j0)/10); end end - }; e& C8 W( `' ~0 i2 X1 Q
U=real(ifft2(FourU)); V=real(ifft2(FourV)); ' Y( K% W# R1 d, E/ E
for i=1:N, for j=1:N, P(i,j)=-U(i,j)*V(i,j)^2+F*(1-U(i,j)); G(i,j)=U(i,j)*V(i,j)^2-(F+K)*V(i,j); end end ( Y; Y) w, |/ ~% N/ ]# T
U = U + dt*P; V = V + dt*G;
; W# R9 i/ X9 _, c! E- Hfor i=1:N, for j=1:N, W(i,j)=V(i,j); M(i,j)=U(i,j); end end ; h8 V$ j( E/ \* |5 x
if rem(compteur,10) == 0 clf; if W>0.6 image(100*W-60); else image(100*W) end if M>0.6 image(100*M-60); else image(100*M); end drawnow; end
9 `7 i6 `: d* G0 {compteur = compteur +1; ; s, U+ g/ B$ P- b& w
end %------------------------------------------
|