Theory and Modern Applications
Table 4 Exact solution and absolute errors for Example 2 at time \(t=1\), \(\beta=1\), fixed \(h=0.0625\) and \(\tau=0.01\)
x | Exact solution | Absolute error | Absolute error |
|---|---|---|---|
FDSF | FVSF | ||
−2. | 0.02949131 | 2.860725 × 10−4 | 8.30618 × 10−5 |
−1.9375 | 0.05741732 | 1.941801 × 10−4 | 9.50135 × 10−5 |
−1.875 | 0.08254919 | 4.107925 × 10−4 | 8.55201 × 10−5 |
−1.8125 | 0.10222554 | 6.965656 × 10−4 | 1.08174 × 10−5 |
−1.75 | 0.12048793 | 1.199878 × 10−4 | 1.27712 × 10−5 |
−1.6875 | 0.13548110 | 1.046201 × 10−4 | 4.48834 × 10−5 |
−1.625 | 0.14885322 | 1.139510 × 10−4 | 6.06044 × 10−5 |
−1.5625 | 0.16225611 | 2.306122 × 10−4 | 7.57187 × 10−5 |
−1.5 | 0.17534557 | 1.393114 × 10−4 | 9.08811 × 10−5 |
−1.4375 | 0.18828164 | 6.647887 × 10−4 | 0.20690 × 10−5 |
−1.375 | 0.20312896 | 3.956443 × 10−4 | 0.70671 × 10−5 |
−1.3125 | 0.21995710 | 8.339676 × 10−4 | 0.84062 × 10−5 |
−1.25 | 0.23504094 | 8.336256 × 10−4 | 0.25998 × 10−5 |