$c=2$

CTCS

Crank-Nicolson

$\omega =0.25$

$\omega =0.5$

Characteristics

$x=0.2$

$h=0.01$

$k=0.001$

Time = 0.031 s

$h=0.01$

$k=0.001$

Time = 7.57 s

$h=0.01$

$k=0.001$

Time = 8.42 s

$h=0.01$

$k=0.001$

Time = 9.08 s

$h=0.01$

$l=0.01$

Time = 0.53 s

$t=0.0$

0.000000%

0.000000%

0.000000%

0.000000%

0.000000%

$t=0.1$

0.001783%

0.015332%

0.004380%

0.000227%

0.008225%

$t=0.2$

0.015189%

0.286670%

0.034187%

0.003179%

0.008225%

$t=0.3$

0.022823%

0.779438%

0.045864%

0.004626%

0.008225%

$t=0.4$

0.007196%

0.509323%

0.011759%

0.002712%

0.008225%

$t=0.5$

0.000012%

0.493089%

0.003096%

0.001108%

0.008222%

$t=0.6$

0.010793%

0.475431%

0.023022%

0.002405%

0.008212%

$t=0.7$

0.053416%

0.196618%

0.101159%

0.017031%

0.008171%

$t=0.8$

0.061050%

1.277865%

0.112325%

0.018414%

0.008279%

$t=0.9$

0.016215%

1.000357%

0.029848%

0.004864%

0.008238%

$t=1.0$

0.000003%

0.981823%

0.000511%

0.000031%

0.008225%

$c=1$

$x=0.3$

CTCS

Crank-Nicolson

$\omega =0.25$

$\omega =0.5$

Characteristics

Time = 0.031 s

Time = 6.93 s

Time = 8.35 s

Time = 8.42 s

Time = 1.05 s

$t=0.0$

0.000000%

0.000000%

0.000000%

0.000000%

0.000000%

$t=0.1$

0.000411%

0.000929%

0.000402%

0.000094%

0.001942%

$t=0.2$

0.001849%

0.008091%

0.001809%

0.000430%

0.004342%

$t=0.3$

0.005263%

0.035146%

0.005149%

0.001232%

0.008225%

$t=0.4$

0.015705%

0.146325%

0.015373%

0.003840%

0.008225%

$t=0.5$

0.005163%

0.064678%

0.004865%

0.001336%

0.000000%

$t=0.6$

0.023579%

0.395394%

0.021686%

0.006576%

0.008225%

$t=0.7$

0.012311%

0.284080%

0.011448%

0.003808%

0.008225%

$t=0.8$

0.007437%

0.256653%

0.007008%

0.002602%

0.008224%

$t=0.9$

0.003745%

0.248873%

0.003595%

0.001602%

0.008223%

$t=1.0$

0.000007%

0.247020%

0.000067%

0.000509%

0.008220%

$c=0.2$

$x=0.4$

CTCS

Crank-Nicolson

$\omega =0.25$

$\omega =0.5$

Characteristics

Time = 0.031 s

Time = 6.3 s

Time = 7.81 s

Time = 7.8 s

Time = 1.79 s

$t=0.0$

0.000000%

0.000000%

0.000000%

0.000000%

0.000000%

$t=0.1$

0.000016%

0.000013%

0.000016%

0.000012%

0.000168%

$t=0.2$

0.000065%

0.000059%

0.000063%

0.000049%

0.000338%

$t=0.3$

0.000147%

0.000146%

0.000143%

0.000110%

0.000510%

$t=0.4$

0.000265%

0.000283%

0.000257%

0.000198%

0.000686%