Theory and Modern Applications
r | Exact solution | Presented method | Absolute error | Method [47] | |
---|---|---|---|---|---|
HBPBP | BP | ||||
\(\underline{{u}} ( {x}, {r} )\) | |||||
0 | 0.000000 | 0.000000 | 8.587086597e−11 | 0.001190 | 0.104322 |
0.1 | 0.050000 | 0.050000 | 6.796341545e−11 | 0.002138 | 0.024766 |
0.2 | 0.100000 | 0.100000 | 5.213430243e−11 | 0.004753 | 0.025467 |
0.3 | 0.150000 | 0.150000 | 3.838351303e−11 | 0.005232 | 0.030005 |
0.4 | 0.200000 | 0.200000 | 2.671108890e−11 | 0.004012 | 0.085691 |
0.5 | 0.250000 | 0.250000 | 1.534772309e−12 | 0.000891 | 0.070301 |
0.6 | 0.300000 | 0.300000 | 8.805067786e−13 | 0.002630 | 0.084357 |
0.7 | 0.350000 | 0.350000 | 4.411249144e−13 | 0.003999 | 0.099502 |
0.8 | 0.400000 | 0.400000 | 2.165712054e−13 | 0.000248 | 0.054350 |
0.9 | 0.450000 | 0.450000 | 1.039095476e−11 | 0.003274 | 0.066229 |
1.0 | 0.500000 | 0.500000 | 1.773514668e−11 | 0.002265 | 0.012674 |
u̅(x,r) | |||||
0 | 1.000000 | 1.000000 | 1.006128514e−11 | 0.002730 | 0.095432 |
0.1 | 0.950000 | 0.950000 | 9.722489480e−12 | 0.001276 | 0.083485 |
0.2 | 0.900000 | 0.900000 | 7.296474536e−12 | 0.001000 | 0.072324 |
0.3 | 0.850000 | 0.850000 | 2.783018260e−12 | 0.008388 | 0.062431 |
0.4 | 0.800000 | 0.800000 | 3.817657301e−12 | 0.001192 | 0.059004 |
0.5 | 0.750000 | 0.750000 | 0.000000000e+00 | 0.002449 | 0.055920 |
0.6 | 0.700000 | 0.700000 | 3.092237577e−12 | 0.008295 | 0.061354 |
0.7 | 0.650000 | 0.650000 | 6.184586177e−12 | 0.002286 | 0.075632 |
0.8 | 0.600000 | 0.600000 | 9.276823754e−12 | 0.000710 | 0.059959 |
0.9 | 0.550000 | 0.550000 | 4.727556124e−11 | 0.005462 | 0.040971 |
1.0 | 0.500000 | 0.500000 | 5.854872143e−11 | 0.001111 | 0.028821 |