$c=2$

Analytical Solution

Approximate Solution

Error

$x=0.2$

$h=0.1$ , $k=0.05$ , $r=1$ , $n=10$ , $m=20$

$t=0.00$

0.58778527

0.58778527

0.000000%

$t=0.05$

0.55901701

0.55901701

0.000000%

$t=0.10$

0.47552826

0.47552826

0.000000%

$t=0.20$

0.18163562

0.18163562

0.000000%

$t=0.30$

−0.18163567

−0.18163567

0.000000%

$t=0.40$

−0.47552829

−0.47552829

0.000000%

$t=0.50$

−0.58778527

−0.58778520

0.000012%

$t=0.60$

−0.47552823

−0.47552821

0.000006%

$t=0.70$

−0.18163557

−0.18163567

0.000054%

$t=0.80$

0.18163571

0.18163562

0.000054%

$t=0.90$

0.47552832

0.47552826

0.000013%

$t=1.00$

0.58778527

0.58778527

0.000000%