Theory and Modern Applications
Table 2 \(L_{2}\) and \(L_{\infty }\) error norms for \(u(x,t)=v(x,t)\) of Example 1 when \(0\leq x\leq 1\), \(\alpha _{1}=\alpha _{2}=0.4\)
N | SJSCM (μ = η = 0, M = N) | Non-polynomial, k = 1/512 | ||
|---|---|---|---|---|
\(L_{2}(U)=L_{2}(V)\) | \(L_{\infty }(U)=L_{\infty }(V)\) | \(L_{2}(U)=L_{2}(V)\) | \(L_{\infty }(U)=L_{\infty }(V)\) | |
6 | 5.111073 × 10−7 | 5.776153 × 10−7 | 4.664657 × 10−6 | 6.426346 × 10−6 |
8 | 7.2802825 × 10−9 | 8.5466062 × 10−9 | 3.26657 × 10−6 | 4.48675 × 10−6 |
10 | 2.0017725 × 10−9 | 2.8590415 × 10−9 | 2.82207 × 10−6 | 3.86984 × 10−6 |
12 | 5.450265 × 10−11 | 8.6848639 × 10−11 | 2.64634 × 10−6 | 3.625546 × 10−6 |