$c=2$ Analytical Solution Approximate Solution Error FD CD BD FD CD BD $x=0.2$ $h=0.1$ , $k=0.05$ , $r=1$ , $n=10$ , $m=20$ , Number of Grid Points = 200 $t=0.000$ 0.58778527 0.58778527 0.58778527 0.58778527 0.000000% 0.000000% 0.000000% $t=0.050$ 0.55901701 0.55877922 0.55970419 0.56062916 0.042536% 0.122926% 0.288391% $t=1.000$ 0.58778527 0.58631380 0.58608352 0.58585324 0.250341% 0.289518% 0.328696% $h=0.1$ , $k=0.001$ , $r=4×{10}^{-4}$ , $n=10$ , $m=1000$ , Number of Grid Points = 10,000 $t=0.000$ 0.58778527 0.58778527 0.58778527 0.58778527 0.000000% 0.000000% 0.000000% $t=0.001$ 0.58777366 0.58777366 0.58777376 0.58777385 0.000000% 0.000016% 0.000032% $t=1.000$ 0.58778527 0.58758962 0.58758923 0.58758884 0.033285% 0.033352% 0.033418% $h=0.01$ , $k=0.005$ , $r=1$ , $n=100$ , $m=200$ , Number of Grid Points = 20,000 $t=0.000$ 0.58778527 0.58778527 0.58778527 0.58778527 0.000000% 0.000000% 0.000000% $t=0.005$ 0.58749523 0.58749521 0.58749522 0.58749532 0.000004% 0.000001% 0.000015% $t=1.000$ 0.58778527 0.58778260 0.58778269 0.58778287 0.000453% 0.000439% 0.000407% $h=0.01$ , $k=0.001$ , $r=4×{10}^{-2}$ , $n=100$ , $m=1000$ , Number of Grid Points = 100,000