Явная схема

function y=k_1(M,N)

h=1/M;

t=1/N;

if t>h

for i=1:10,disp(' ');end;

disp(' ВОЗМОЖНА НЕУСТОЙЧИВОСТЬ!!!');

disp('(невыполнено условие устойчивости Куранта-Леви:t<=h)!!!');

pause

end;

t2=t^2;

h2=h^2;

g=t2/h2;

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

S=zeros(M+1);

for j=1:N+1

U(M+1,j)=0;

end;

U(1:M,1)=-sin(2*(1:M)'*h*pi);

U(1:M,2)=U(1:M,1)-t*sin(2*(1:M)'*h*pi);

f=@(x,t)sin(2*h*pi).*(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));

for k=2:N

U(2:M,k+1)=g^2*U(3:M+1,k)+2*(1-g^2)*U(2:M,k)+...

g^2*U(1:M-1,k)-U(2:M,k-1)+t^2*f((2:M)'*h*pi,k*t*pi/2^.5);

end;

U(1,3:N+1)=U(2,3:N+1)-2*h./((3:N+1)*t-1);

mesh(U);end

Построение двумерных параметрических графиков

u[10x10]

-0.2694 -0.6292 -0.7352 -0.6487 -0.4149 -0.1136 0.1764	0.4006 0.5376 0.5940 0
-0.5657 -1.0067 -1.1763 -1.0379 -0.6638 -0.1817 0.2822	0.6410 0.8601 0.9505 0
-0.8179 -1.2694 -1.3558 -1.1293 -0.6869 -0.1517 0.3599	0.7664 1.0330 1.1682 0
-0.8038 -1.1852 -1.1898 -0.9271 -0.5137 -0.0484 0.3946	0.7670 1.0466 1.2350 0
-0.4953 -0.7068 -0.6751 -0.4859 -0.2180 0.0787 0.3788	0.6688 0.9392 1.1824 0
-0.0018 0.0195 0.0470 0.0768 0.1205 0.1987 0.3305	0.5247 0.7763 1.0666 0
0.4883 0.7267 0.7334 0.5996 0.4309 0.3112 0.2936	0.4010 0.6287 0.9476 0
0.7793 1.1374 1.1415 0.9353 0.6597 0.4263 0.3121	0.3556 0.5549 0.8730 0
0.7267 1.0778 1.1461 1.0115 0.7699 0.5343 0.4006	0.4187 0.5875 0.8681 0
0.2255 0.5925 0.8181 0.8346 0.7232 0.5983 0.5409	0.5836 0.7208 0.9249 0
-1.0002 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000	0.8000 0.9000 1.0000 0