# Table 1 Numerical results of the FRPS solutions at different values of t of Example 4.1

t Exact u(t) Approximation u(t) Absolute Error Relative Error
0.000 1. 1. 0. 0.
0.025 1.830049650419 1.8300496504186 6.661338147751 × 10−16 3.639976732996 × 10−16
0.050 1.820521847980 1.8205218479801 4.218847493576 × 10−15 2.317383610780 × 10−15
0.075 1.7389664179059 1.7389664179059 1.998401444325 × 10−15 1.149189210181 × 10−15
0.100 1.6548121396395 1.6548121396396 6.017408793468 × 10−14 3.636309312294 × 10−14
0.125 1.574165520630 1.5741655206310 1.418198891656 × 10−12 9.009210740996 × 10−13
0.150 1.4973979619154 1.4973979619805 6.508638072944 × 10−11 4.346632116834 × 10−11
0.175 1.4243694914073 1.4243694910746 3.326674491433 × 10−10 2.335541803936 × 10−10
0.200 1.3549022160256 1.3549022084615 7.564062487475 × 10−9 5.582736818944 × 10−9
0.225 1.2888228592360 1.2888227498472 1.093887884718 × 10−7 8.487495988131 × 10−8
0.250 1.2259662270401 1.2259657966770 4.303631988556 × 10−7 3.510400118400 × 10−7
t Exact v(t) Approximation v(t) Absolute Error Relative Error
0.000 1. 1. 0. 0.
0.025 0.0724091985828 0.0724091985828 2.3592239273 × 10−16 3.2581826253 × 10−15
0.050 −0.010847011908 −0.010847011908 3.2734231992 × 10−15 3.0178110130 × 10−13
0.075 −0.0175504650558 −0.0175504650558 1.3850032232 × 10−14 7.8915471403 × 10−13
0.100 −0.0173506334835 −0.0173506334839 3.6409417148 × 10−13 2.0984488654 × 10−11
0.125 −0.0165639544868 −0.0165639544956 8.8100464424 × 10−12 5.3188062364 × 10−10
0.150 −0.0157615205520 −0.0157615206823 1.3034362131 × 10−10 8.2697364688 × 10−9
0.175 −0.0149933119699 −0.0149933122356 2.6574836429 × 10−10 1.7724460401 × 10−8
0.200 −0.0142621239543 −0.0142621227122 1.2421122308 × 10−9 8.7091672654 × 10−8
0.225 −0.0135665559925 −0.0135665780247 2.2032217302 × 10−8 1.6240096100 × 10−6
0.250 −0.0129049076149 −0.0129052984430 3.9082809609 × 10−7 3.0285230070 × 10−5