Theory and Modern Applications
Table 1 \(L_{2}\) and \(L_{\infty }\) error norms for \(u(x,t)=v(x,t)\) of Example 1 when \(0\leq x\leq 1\), \(\alpha _{1}=\alpha _{2}=0.1\)
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 | 5.1510654 × 10−7 | 5.7880948 × 10−7 | 2.422437 × 10−6 | 3.370818 × 10−6 |
8 | 7.01838 × 10−9 | 9.0064422 × 10−9 | 9.61156 × 10−7 | 1.334979 × 10−6 |
10 | 4.531374 × 10−10 | 6.070393 × 10−10 | 4.964396 × 10−7 | 6.874885 × 10−7 |
12 | 1.6627626 × 10−10 | 2.6921354 × 10−10 | 3.126976 × 10−7 | 4.317349 × 10−7 |