Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting

Haar	Euler	Haar	Euler
k=21.97e−3	1.05e−6	4.71e−4	2.28e−7
k=34.91e−4	6.99e−8	1.65e−4	1.97e −8
k=41.23e−4	6.41e−9	5.84e−5	2.79e −9
k=53.12e−5	4.32e−10	2.06e−5	2.72e −10
k=68.92e−6	2.75e−11	7.28e−6	2.46e −10
k=72.96e−6	1.73e−12	2.56e−6	2.19e −11
k=81.29e−7	1.08e−13	8.81e−7	1.93e −12

Error method	L∞	L∞	L2	L2

k=1	Haar	Euler	Haar	Euler
k=2	7.80e−4	5.36e−5	1.63e−3	1.68e−4
k=3	1.94e −4	3.97e−6	5.74e−4	1.21e −5
k=4	4.84e −5	2.73e−7	2.03e−4	8.57e −7
k=5	1.21e −5	1.76e−8	7.18e−5	5.50e −8
k=6	3.02e −6	1.17e−9	2.54e−5	3.66e −9
k=7	7.55e −7	7.39e−11	8.97e−6	2.32e −10
k=8	1.89e −7	4.59e−12	3.17e−6	1.44e −11

x			k=2, M=4	k=3, M=5	k=5, M=6

0	0.693147180559945		0.693147180559945	0.693147180559945	0.693147180559945
0.1	0.683196849706777		0.683227245796262	0.683197075022063	0.683196849437443
0.2	0.653926467406664		0.653969148173502	0.653926783980363	0.653926466991036
0.3	0.606969484318893		0.607019006611345	0.606969843582379	0.606969483813016
0.4	0.544727175441672		0.544780344557389	0.544727529512898	0.544727174911210
0.5	0.470003629245736		0.470056791556372	0.470003963513028	0.470003628756537
0.6	0.385662480811985		0.385704191793314	0.385662747357822	0.385662480415734
0.7	0.294371060602578		0.294402255148925	0.294371256591398	0.294371060311363
0.8	0.198450938723838		0.198471255975016	0.198451064512775	0.198450938537864
0.9	0.099820335282211		0.099829667365162	0.099820397248811	0.099820335194224
1.0		0	0	0	0

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