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| MATLAB utilities |
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- Solution to scalar linear conservation law with initial data
- ramp.m
- mycubic.m
- myerf.m
- myrunge.m
(You will need the function translate .)
Use for t=0:.1:2 translate(t,@myerf,0);pause(0.05);end
- Solution to Burgers' equation with initial data as above
Use for t=0:.1:2 translate(t,@myerf,1);pause(0.05);end
- Non-uniqueness or non-existence of solutions to Burger's
equation seen as a result of solving the fixed point problem x_0=h(x_0).
Use fixed_fun.m and x0 = -4:.1:4;
- To see unique solution xo (interesection of y=x0 and y=h(x_0))
for x=1/2, t=1/2
plot(x0, x0, '-',x0,fixed_fun(1/2,1/2,x0,@ramp),'*')
- To see nonunique solution for x=1,t=1
plot(x0, x0, '-',x0,fixed_fun(1/2,1/2,x0,@ramp),'*')
- To see nonunique solution for x=1,t=2
plot(x0, x0, '-',x0,fixed_fun(1,2,x0,@ramp),'*')
- Utiltities for visualizing acoustic waves can be found at a website
for
R. LeVeque's book on "Finite Volume methods for Hyperbolic Problems" (denoted below as RLV)
- Revisit the solution to the IVP for the second-order wave equation
from MTH 621 wave.m and compare it to the one given by
wave_acoustic.m. Notice the formation of intermediate states
for the Riemann problem.
- Visualize velocity fields from class examples using MATLAB. For example, simple example:
[x1,x2]=meshgrid(-10:1:10,-10:1:10);
v1 = x1; v2 = -x2;
quiver(x1,x2,v1,v2);
or a more complicated example:
[x1,x2]=meshgrid(-10:1:10,-10:1:10);
v1 = x1./(x1.^2+x2.^2); v2 = -x2./(x1.^2+x2.^2);
quiver(x1,x2,v1,v2);
- Visualize (Wikipedia)
P-wave
and
S-wave.
and deformation of a plate (RLV)
- Deformation in non-homogeneous media
elastic wave propagating in a medium with stiff inclusion (RLV)
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