Table 1 Example 4.1, maximum absolute errors for the case \(\tau = 0.5\varepsilon\)
From: Fitted computational method for solving singularly perturbed small time lag problem
\(\varepsilon \downarrow\) | N = M =16 | 32 | 64 | 128 | 256 |
|---|---|---|---|---|---|
\(2^{-0}\) | 1.3260e−03 | 7.4390e−04 | 3.9431e−04 | 2.0293e−04 | 1.0294e−04 |
\(2^{-2}\) | 1.3097e−02 | 7.2784e−03 | 3.8340e−03 | 1.9676e−03 | 9.9661e−04 |
\(2^{-4}\) | 2.7648e−02 | 1.5726e−02 | 8.3824e−03 | 4.3310e−03 | 2.2011e−03 |
\(2^{-6}\) | 3.7674e−02 | 1.9780e−02 | 1.0209e−02 | 5.3769e−03 | 2.7671e−03 |
\(2^{-8}\) | 3.7154e−02 | 2.2029e−02 | 1.2040e−02 | 5.6488e−03 | 2.8289e−03 |
\(2^{-10}\) | 3.7206e−02 | 2.1942e−02 | 1.1903e−02 | 6.2248e−03 | 3.1986e−03 |
\(2^{-12}\) | 3.7221e−02 | 2.1951e−02 | 1.1906e−02 | 6.1986e−03 | 3.1627e−03 |
\(2^{-14}\) | 3.7224e−02 | 2.1953e−02 | 1.1907e−02 | 6.1992e−03 | 3.1627e−03 |
\(2^{-16}\) | 3.7225e−02 | 2.1953e−02 | 1.1907e−02 | 6.1993e−03 | 3.1627e−03 |
\(2^{-18}\) | 3.7225e−02 | 2.1953e−02 | 1.1908e−02 | 6.1994e−03 | 3.1627e−03 |
\(2^{-20}\) | 3.7225e−02 | 2.1953e−02 | 1.1908e−02 | 6.1994e−03 | 3.1627e−03 |
Proposed scheme | Â | Â | Â | Â | Â |
\(E^{N,M}\) | 3.7225e−02 | 2.2029e−02 | 1.2040e−02 | 6.2248e−03 | 3.1986e−03 |
\(r^{N,M}\) | 0.77417 | 0.87156 | 0.95174 | 0.96059 | – |
Method in [14] | Â | Â | Â | Â | Â |
\(E^{N,M}\) | 8.3951e−02 | 4.9224e−02 | 2.6666e−02 | 1.3880e−02 | 7.0816e−03 |
\(r^{N,M}\) | 0.77019 | 0.88436 | 0.94199 | 0.97086 | – |