Неявная схема

function y=k_2(M,N)

h=1/M; t=1/N;

u=zeros(M+1,N+1);

h2=h^2; t2=t^2; g2=t2/h2;

for j=1:N+1

u(M+1,j)=0;

end;

A=zeros(M,1);C=zeros(M+1,1);B=A;A1=A;F=C;B1=C;

for i=1:M

A(i)=g2/2;

B(i+1)=g2/2;

C(i+1)=1+g2;

F(i+1)=-10*sin(2*i*h*pi);

end;

A(M)=0; B(1)=0;

C(1)=1+h*g2+g2;

C(M+1)=1;

F(1)=0; F(M+1)=0;

A1(1)=B(1)/C(1);

B1(1)=F(1)/C(1);

for i=2:M

A1(i)=B(i)/(C(i)-A(i-1)*A1(i-1));

B1(i)=(F(i)+A(i-1)*B1(i-1))/(C(i)-A(i-1)*A1(i-1));

end;

B1(M+1)=(F(M+1)+A(M)*B1(M))/(C(M+1)-A(M)*A1(M));

u(M+1,2)=B1(M+1);

for i=M:-1:1

u(i,2)=A1(i)*u(i+1,2)+B1(i);

end;

for i=1:M-1

A(i)=g2; B(i+1)=g2;

C(i+1)=1+2*g2;

end

A(M)=0; B(1)=2*g2;

C(1)=1+2*h*g2+2*g2;

C(M+1)=1;

A1(1)=B(1)/C(1);

B1(1)=F(1)/C(1);

F(1)=0;

for j=2:N

for i=1:M-1

F(i+1)=2*u(i+1,j)-u(i+1,j-1)+5*t2*sin(2*i*pi*h)*(2*pi*pi*t2-4*pi*t*sqrt(2)+5)/(0.5*pi*pi*pi*t*t*t-(3*pi*pi*t2/sqrt(2))+3*pi*t-1/sqrt(2));

end;

for i=2:M

A1(i)=B(i)/(C(i)-A(i-1)*A1(i-1));

B1(i)=(F(i)+A(i-1)*B1(i-1))/(C(i)-A(i-1)*A1(i-1));

end;

F(M+1)=0;

B1(M+1)=(F(M+1)+A(M)*B1(M))/(C(M+1)-A(M)*A1(M));

u(M+1,j+1)=B1(M+1);

for i=M:-1:1

u(i,j+1)=A1(i)*u(i+1,j+1)+B1(i);

end;

end;

contour(u,20);pause;

for j=0:N,

i=1:1:M;

u1=u(i,j+1);

plot(i,u1);

end;

mesh(u); end

Построение двумерных параметрических графиков

u[10x10]

0.0514 -0.3180 -0.3556 -0.2176 0.0462 0.3547 0.6299	0.8213 0.9133 0.9210 0
-0.4797 -0.8027 -0.8629 -0.6421 -0.2199 0.2736 0.7140	1.0201 1.1674 1.1798 0
-0.7949 -1.1599 -1.1368 -0.8150 -0.3141 0.2345 0.7155	1.0554 1.2333 1.2741 0
-0.7976 -1.1350 -1.0700 -0.7368 -0.2767 0.1955 0.6019	0.9020 1.0895 1.1840 0
-0.4933 -0.6975 -0.6483 -0.4379 -0.1599 0.1210 0.3749	0.5949 0.7855 0.9533 0
0.0001 -0.0003 -0.0027 -0.0070 -0.0052 0.0202 0.0913	0.2247 0.4227 0.6704 0
0.4935 0.6965 0.6407 0.4221 0.1557 -0.0570 -0.1466	-0.0833 0.1245 0.4373 0
0.7986 1.1321 1.0548 0.7176 0.2982 -0.0511 -0.2322	-0.2089 0.0001 0.3387 0
0.7985 1.1503 1.1055 0.8009 0.4061 0.0724 -0.1019	-0.0826 0.1091 0.4172 0
0.4935 0.7693 0.8071 0.6721 0.4713 0.3045 0.2355	0.2848 0.4380 0.6596 0
0.0000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000	0.8000 0.9000 1.0000 0