Theory and Modern Applications

# Table 2 Exact solution and absolute errors for Example 1 at time $$t=1$$, $$\beta=1$$, fixed $$h=0.015625$$ and $$\tau=0.01$$ using FDSF and FVSF

x Exact solution Absolute error Absolute error
FDSF FVSF
1. 0. 7.193791 × 10−5 5.814751 × 10−6
1.015625 −1.312701 × 10−10 1.438076 × 10−5 1.162322 × 10−7
1.03125 −2.622240 × 10−10 2.1553847 × 10−5 1.741653 × 10−7
1.046875 −3.925462 × 10−10 2.8706087 × 10−5 2.318803 × 10−7
1.0625 −5.219227 × 10−10 3.5830568 × 10−5 2.893150 × 10−7
1.078125 −6.500419 × 10−10 4.2920399 × 10−5 3.464091 × 10−7
1.09375 −7.765951 × 10−10 4.9968719 × 10−5 4.031040 × 10−7
1.109375 −9.012773 × 10−10 5.696871 × 10−5 4.593420 × 10−7
1.125 −1.023788 × 10−9 6.391360 × 10−5 5.150668 × 10−7
1.140625 −1.143833 × 10−9 7.079666 × 10−5 5.702229 × 10−7
1.15625 −1.261122 × 10−9 7.761125 × 10−5 6.247557 × 10−7
1.171875 −1.375372 × 10−9 8.435077 × 10−5 6.786116 × 10−7
1.1875 −1.486310 × 10−9 9.100869 × 10−5 7.317379 × 10−7
1.203125 −1.593667 × 10−9 9.757858 × 10−5 7.840830 × 10−7
1.21875 −1.697184 × 10−9 10.40540 × 10−5 8.355962 × 10−7
1.234375 −1.796613 × 10−9 11.04289 × 10−5 8.862276 × 10−7
1.25 −1.891714 × 10−9 11.66969 × 10−5 9.359287 × 10−7