```
D03PLF Example Program Results

Example 1

Method Parameters:
Number of mesh points used =  201
Relative tolerance used    =  0.250E-03
Absolute tolerance used    =  0.100E-04

Integration Results:
Global error is less than 100 times the local error tolerance.

Integration Statistics:
Number of time steps           (nearest  50) =    150
Number of function evaluations (nearest 100) =   1400
Number of Jacobian evaluations (nearest  20) =     20
Number of iterations           (nearest 100) =    400

Example 2

Problem Parameter and initial conditions:
gamma          = 1.400
e(x<0.5,0) = 2.500    e(x>0.5,0) = 0.250
rho(x>0.5,0) = 1.000  rho(x>0.5,0) = 0.125

Method Parameters:
Number of mesh points used =  141
Relative tolerance used    =  0.500E-03
Absolute tolerance used    =  0.500E-02

Solution
t      x     density velocity pressure
0.100  0.0000   1.0000   0.0000   1.0000
0.100   1.0000  -0.0000   1.0000
0.200   1.0000  -0.0000   1.0000
0.300   1.0000  -0.0000   1.0000
0.400   0.8668   0.1665   0.8188
0.500   0.4299   0.9182   0.3071
0.600   0.2969   0.9274   0.3028
0.700   0.1250   0.0000   0.1000
0.800   0.1250  -0.0000   0.1000
0.900   0.1250  -0.0000   0.1000
1.000   0.1250   0.0000   0.1000

0.200  0.0000   1.0000   0.0000   1.0000
0.100   1.0000  -0.0000   1.0000
0.200   1.0000  -0.0000   1.0000
0.300   0.8718   0.1601   0.8253
0.400   0.6113   0.5543   0.5022
0.500   0.4245   0.9314   0.3014
0.600   0.4259   0.9277   0.3030
0.700   0.2772   0.9272   0.3031
0.800   0.2657   0.9276   0.3032
0.900   0.1250  -0.0000   0.1000
1.000   0.1250   0.0000   0.1000

Number of time steps           (nearest 50) =    150
Number of function evaluations (nearest 50) =    400
Number of Jacobian evaluations (nearest  1) =      1
Number of iterations           (nearest  1) =      2
```