Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind

Table 1

Some numerical results for Example 6.1.

$x$	Exact solution	Approximate solution $k=2,M=2,{\varepsilon }_0=10^{-5}$	Approximate solution $k=2,M=4,{\varepsilon }_0=10^{-4}$	Legendre wavelets [15]
$0.0$	$0.0000000000$	$0.0000000002$	$-$0.0000080915	$-$0.0000623203
$0.1$	$0.1000000000$	$0.0999467145$	$0.0999919084$	$0.0999399803$
$0.2$	$0.2000000000$	$0.1998628369$	$0.1999919083$	$0.1999422810$
$0.3$	$0.3000000000$	$0.2997789593$	$0.2999919083$	$0.2999445816$
$0.4$	$0.4000000000$	$0.3996950817$	$0.3999919082$	$0.3999468823$
$0.5$	$0.5000000000$	$0.4994017104$	$0.4999821126$	$0.5000836748$
$0.6$	$0.6000000000$	$0.5996197220$	$0.5999908426$	$0.6000583321$
$0.7$	$0.7000000000$	$0.6994489377$	$0.6999914808$	$0.7000329894$
$0.8$	$0.8000000000$	$0.7992781533$	$0.7999921190$	$0.8000076466$
$0.9$	$0.9000000000$	$0.8991073690$	$0.8999927572$	$0.8999823039$
$1.0$	$1.0000000000$	$0.9989365847$	$0.9999933955$	$0.9999569612$