Theory and Modern Applications
Table 1 The maximum absolute errors
γ(x,t) | Method [43] | Proposed method | ||
|---|---|---|---|---|
\(\tau ^{2} = h^{2} = \frac{1}{{256}}\) | N = M = 4 | N = M = 8 | N = M = 12 | |
\(\frac{10-xt}{300} \) | 1.1311 × 10−4 | 41806 × 10−5 | 4.8553 × 10−11 | 6.5749 × 10−16 |
\(\frac{20-e^{xt}}{600}\) | 9.2323 × 10−5 | 4.1813 × 10−5 | 4.8554 × 10−11 | 9.9033 × 10−16 |
\(\frac{12+x^{3}-t^{5}}{300}\) | 3.7142 × 10−4 | 4.1810 × 10−5 | 3.9710 × 10−11 | 6.0284 × 10−16 |
\(\frac{15+\cos (xt)}{450}\) | 3.7155 × 10−5 | 4.1810 × 10−5 | 3.9711 × 10−11 | 5.4710 × 10−16 |
\(\frac{10-\sin (xt)}{310}\) | 9.6551 × 10−5 | 4.1808 × 10−5 | 4.8554 × 10−11 | 7.0597 × 10−16 |
\(\frac{10+(xt)^{2}-(xt)^{3}}{300}\) | 1.2258 × 10−5 | 4.1808 × 10−5 | 4.8552 × 10−11 | 6.9103 × 10−16 |
\(\frac{13-xt+\cos (xt)}{400}\) | 1.6057 × 10−4 | 4.1804 × 10−5 | 4.8551 × 10−11 | 6.0096 × 10−16 |
\(\frac{11+(xt)^{2}-\sin (xt)}{330}\) | 2.0982 × 10−5 | 4.1815 × 10−5 | 4.8553 × 10−11 | 5.3889 × 10−16 |
\(\frac{18-sin^{2}(xt)+\cos ^{3}(xt)}{630}\) | 9.0181 × 10−5 | 4.1785 × 10−5 | 4.8618 × 10−11 | 4.9293 × 10−16 |