求解二阶双曲型方程的自适应网格方法

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CLC Number:

O241.82

Qin Zhou,Yin Yang. Adaptive Mesh Method for Solving a Second-Order Hyperbolic Equation[J].Acta mathematica scientia,Series A, 2019, 39(4): 942-950.

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$N\times M$	$t=0.5$	$ r$	$ t=1$	$ r$	$ t=1.5$	$ r$	$ t=2$	$ r$
$50\times50$	9.508E-05		2.797E-04		5.684E-04		9.174E-04
$100\times100$	2.530E-05	1.91	8.225E-05	1.77	1.684E-04	1.76	2.673E-04	1.78
$200\times200$	8.934E-06	1.50	2.225E-05	1.89	4.630E-05	1.86	7.321E-05	1.87

$N\times M$	$t=0.5$	$r$	$ t=1$	$ r$	$t=1.5$	$ r$	$t=2$	$r$
$50\times50$	1.952E-04		7.678E-04		1.480E-03		2.196E-03
$100\times100$	5.472E-05	1.83	2.433E-04	1.66	4.720E-04	1.65	6.970E-04	1.66
$200\times200$	2.099E-05	1.38	6.838E-05	1.83	1.354E-04	1.80	1.999E-04	1.80

$N\times M$	$t=0.5$	$t=1$	$ t=1.5$	$ t=2$
$50\times50$	7.683E-04	2.571E-03	4.787E-03	6.949E-03
$100\times100$	3.513E-04	1.113E-03	1.902E-03	2.499E-03
$200\times200$	1.127E-04	3.276E-04	5.221E-04	6.652E-04

$N\times M$	$t=0.5$	$t=1$	$ t=1.5$	$t=2$
$50\times50$	5.433E-03	1.813E-02	3.353E-02	4.808E-02
$100\times100$	3.256E-03	1.001E-02	1.596E-02	1.834E-02
$200\times200$	1.201E-03	2.842E-03	4.560E-03	5.417E-03

$N\times M$	$t=0.5$	$r$	$t=1$	$r$	$ t=1.5$	$ r$	$ t=2$	$r$
$50\times50$	1.622E-04		2.400E-04		4.571E-04		6.861E-04
$100\times100$	4.274E-05	1.92	5.581E-05	2.10	1.147E-04	1.99	1.750E-04	1.97
$200\times200$	1.948E-05	1.13	1.698E-05	1.72	2.800E-05	2.03	4.703E-05	1.90

Adaptive Mesh Method for Solving a Second-Order Hyperbolic Equation

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References 13

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$N\times M$	$ t=0.5$	$ r$	$ t=1$	$ r$	$t=1.5$	$ r$	$ t=2$	$ r$
$50\times50$	1.952E-04		7.678E-04		1.480E-03		2.196E-03
$100\times100$	5.472E-05	1.83	2.433E-04	1.66	4.720E-04	1.65	6.970E-04	1.66
$200\times200$	2.099E-05	1.38	6.838E-05	1.83	1.354E-04	1.80	1.999E-04	1.80

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