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MATHEMATICS 2ZZ3: Animations
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to see the solution of the wave equation on the whole line.
The initial condition is u(x,0)=1 for x between -1 and 1 and u(x,0)=0 otherwise
as well as u_t(x,0)=0 for all x.
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to see the solution of the wave equation on the whole line.
The initial condition is u(x,0)=0 for all x and u_t(x,0)=1 for x between -1 and 1, u_t(x,0)=0 otherwise
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to see the solution of the wave equation on a semi-infinite string.
The initial condition is u(x,0)=1 for x between 2 and 3 and u(x,0)=0 otherwise
as well as u_t(x,0)=0 for all x.
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to see the solution of the wave equation on a semi-infinite string.
The initial condition is u_t(x,0)=1 for x between 2 and 3 and u_t(x,0)=0 otherwise
as well as u(x,0)=0 for all x.
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to see an animation of the first three standing waves.
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to see the solution of the wave equation on a finite string from x=0 to x=10.
The initial condition is u(x,0)=1 for x between 2 and 3 and u(x,0)=0 otherwise
as well as u_t(x,0)=0 for all x.
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to see the solution of the wave equation on a rectangle where x varies from 0 to 1
and y from 0 to 2 with u=0 on the boundary. Initially the displacement of the menbrane is given by
u(x,y,0)= sin(pi x) and u_t(x,y,0)=0.
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to see the solution of the heat equation u_t=u_xx+Q(x) for 0< x < pi, u(0,t)=u(pi,t)=0,
u(x,0)=sin x where Q(x)=0 for 0< x < pi/2 and Q(x)=1 for pi/2< x < pi.
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to see the solution of the wave equation on the half-line x>0 u_tt=4 u_xx
with boundary condition u(0,t)=0 and initial condition u(x,0)=1+sin x,
u_y(x,0)=cos x.
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to see the solution of the PDE u_t+x exp(-t) u_x=0 on the whole real line with initial condition
u(x,0)=1+x^2
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to see the solution of the PDE u_t+ 3 t^2 u_x= t (1+u^2) with initial condition
u(x,0)=f(x) where f(x)=0, x<0; f(x)=x, 01.
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to see the solution of the quasi-linear equation u_t+ u u_x=0 with initial condition
u(x,0)=f(x) and f(x)=0 for x negative, f(x)=x for x between 0 and 1 and f(x)=1 for x larger
than 1.
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to see the solution of the quasi-linear equation solution of the traffic flow equation
u_t+ (1-u/2) u_x=0 with initial condition
u(x,0)=f(x) and f(x)=4 for x negative, f(x)=0 for x larger
than 0.
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to see the typical motion of 3 cars stopped behind each other at a red light
when the light turns green at time t=0. The PDE and IC are the same as in the previous example.
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to see the solution of the quasi-linear equation solution of the traffic flow equation
u_t+ (1-u/2) u_x=0 with initial condition
u(x,0)=f(x) and f(x)=0 for x negative, f(x)=x in (0,2) and f(x)=2 for x larger then 2.
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to see the solution of the quasi-linear equation solution of the traffic flow equation
u_t+ (1-u/2) u_x=0 with initial condition
u(x,0)=f(x) and f(x)=4 for x negative, f(x)=0 in (0,10), f(x)=4 in (10,20) and f(x)=0 for x larger then 20.
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to see the solution of the quasi-linear equation solution of the traffic flow equation
u_t+ (1-u/2) u_x=0 with initial condition
u(x,0)=f(x) and f(x)=1 for x negative, f(x)=2 in (0,1), and f(x)=3 for x larger then 1.
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to see the solution of the quasi-linear equation solution of the traffic flow equation
u_t+ (1-u/2) u_x=0 with initial condition
u(x,0)=f(x) and f(x)=1 for x negative, f(x)=3 in (0,1), and f(x)=2 for x larger then 1.
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to see the solution of the quasi-linear equation solution of the traffic flow equation
u_t+ (1-u/2) u_x=0 with initial condition
u(x,0)=f(x) and f(x)=3 for x negative, f(x)=2 in (0,1), and f(x)=1 for x larger then 1.
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PICTURES
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of the heat equation.
