Theory and Modern Applications

# Table 1 Numerical results for Example 1 with varying β at time $$t=1$$, fixed $$h=0.015625$$ and $$\tau=0.01$$ using FDSF and FVSF

x β = 0.7 β = 0.8 β = 0.9
FDSF FVSF FDSF FVSF FDSF FVSF
1. 2.8695 × 10−4 3.2270 × 10−4 3.0669 × 10−4 2.2835 × 10−4 1.2079 × 10−4 4.0124 × 10−5
1.015625 5.7376 × 10−4 6.4525 × 10−4 6.1325 × 10−4 4.5659 × 10−4 2.4151 × 10−4 8.0218 × 10−5
1.03125 8.6030 × 10−4 9.6750 × 10−4 9.1951 × 10−4 6.8460 × 10−4 3.6208 × 10−4 12.0254 × 10−5
1.046875 1.14637 × 10−3 12.8924 × 10−4 1.22528 × 10−3 9.1221 × 10−4 4.8242 × 10−4 16.0196 × 10−5
1.0625 1.43177 × 10−3 16.1023 × 10−4 1.53032 × 10−3 11.3925 × 10−4 6.0243 × 10−4 20.0010 × 10−5
1.078125 1.71627 × 10−3 19.3022 × 10−4 1.83439 × 10−3 13.6553 × 10−4 7.2200 × 10−4 23.9660 × 10−5
1.09375 1.99964 × 10−3 22.4893 × 10−4 2.13724 × 10−3 15.9087 × 10−4 8.4103 × 10−4 27.9109 × 10−5
1.109375 2.28164 × 10−3 25.6612 × 10−4 2.43861 × 10−3 18.1505 × 10−4 9.5941 × 10−4 31.8321 × 10−5
1.125 2.56202 × 10−3 28.8149 × 10−4 2.73823 × 10−3 20.3789 × 10−4 10.7703 × 10−4 35.7259 × 10−5
1.140625 2.84055 × 10−3 31.9476 × 10−4 3.03583 × 10−3 22.5918 × 10−4 11.9379 × 10−4 39.5886 × 10−5
1.15625 3.11696 × 10−3 35.0567 × 10−4 3.33115 × 10−3 24.7871 × 10−4 13.0957 × 10−4 43.4166 × 10−5
1.171875 3.39102 × 10−3 38.1392 × 10−4 3.62391 × 10−3 26.9629 × 10−4 14.2428 × 10−4 47.2062 × 10−5
1.1875 3.66247 × 10−3 41.1923 × 10−4 3.91384 × 10−3 29.1171 × 10−4 15.3779 × 10−4 50.9538 × 10−5
1.203125 3.93106 × 10−3 44.2132 × 10−4 4.20068 × 10−3 31.2477 × 10−4 16.5000 × 10−4 54.6558 × 10−5
1.21875 4.19653 × 10−3 47.1990 × 10−4 4.48415 × 10−3 33.3527 × 10−4 17.6081 × 10−4 58.3087 × 10−5
1.234375 4.45864 × 10−3 50.14697 × 10−4 4.76397 × 10−3 35.4299 × 10−4 18.7011 × 10−4 61.9088 × 10−5
1.25 4.71715 × 10−3 53.0542 × 10−4 5.03990 × 10−3 37.4776 × 10−4 19.7778 × 10−4 65.4528 × 10−5