Dalamber usuli (xarakteristik usul) Tor tebranish tenglamasi. Dalamber formulasi

a:=1;L:=1;alpha:=1;

u1(t,x):=1/2*PIECEWISE([0, x-a*t < -L],[alpha*(1+(x-a*t)/L), x-a*t < 0],[alpha*(1-(x-a*t)/L), x-a*t < L],[0, L < x-a*t]);

u2(t,x):=1/2*PIECEWISE([0, x+a*t < -L],[alpha*(1+(x+a*t)/L), x+a*t < 0],[alpha*(1-(x+a*t)/L), x+a*t < L],[0, L < x+a*t]);

u(t,x):=1/2*PIECEWISE([0, x-a*t < -L],[alpha*(1+(x-a*t)/L), x-a*t < 0],[alpha*(1-(x-a*t)/L), x-a*t < L],[0, L < x-a*t])+1/2*PIECEWISE([0, x+a*t < -L],[alpha*(1+(x+a*t)/L), x+a*t < 0],[alpha*(1-(x+a*t)/L), x+a*t < L],[0, L < x+a*t]);

animate(plot,[u1(t,x),x=-5..5, y=-0.1..1], t=0..4, frames=30,thickness=3, title="u1(t,x)");

animate(plot,[u2(t,x),x=-5..5, y=-0.1..1], t=0..4, frames=30,thickness=3, title="u2(t,x)");

animate(plot,[u(t,x),x=-5..5, y=-0.1..1], t=0..4, frames=30,thickness=3, title="u(t,x)");

animate(plot,[{u1(t,x),u2(t,x),u(t,x)},x=-5..5, y=-0.1..1], t=0..4, frames=30,thickness=3, title="u1(t,x), u2(t,x), u(t,x)");

Warning, the name changecoords has been redefined

Olingan yechimni vaqtni bir nechta momentlari uchun ikki o'lchamli grafik ko'rinishda tasvirlaymiz:

> tau:=3: