Table 3 Comparison of rate of convergence for Example 1
From: Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
\(\varepsilon \downarrow \,M/N \to\) | 32/20 | 64/40 | 128/80 | 256/160 |
|---|---|---|---|---|
After extrapolation | Â | Â | Â | |
\(2^{ - 6}\) | 1.9098 | 1.9894 | 1.7283 | 1.6506 |
\(2^{ - 8}\) | 1.8727 | 1.9458 | 1.9784 | 1.9936 |
\(2^{ - 10}\) | 1.8710 | 1.9392 | 1.9706 | 1.9868 |
\(2^{ - 12}\) | 1.8715 | 1.9350 | 1.9696 | 1.9852 |
\(2^{ - 18}\) | 1.8713 | 1.9339 | 1.9692 | 1.9845 |
Before extrapolation | Â | Â | Â | |
\(2^{ - 6}\) | 0.8839 | 0.9566 | 0.9989 | 1.0228 |
\(2^{ - 8}\) | 0.8839 | 0.9566 | 0.9989 | 1.0228 |
\(2^{ - 10}\) | 0.8769 | 0.9385 | 0.9695 | 0.9851 |
\(2^{ - 12}\) | 0.8778 | 0.9388 | 0.9686 | 0.9846 |
\(2^{ - 18}\) | 0.8782 | 0.9390 | 0.9679 | 0.9845 |
Results in [6] | Â | Â | Â | Â |
\(2^{ - 6}\) | 0.5170 | 0.9724 | 0.8966 | 0.9504 |
\(2^{ - 8}\) | 0.9856 | 0.7971 | 0.8362 | 0.9119 |
\(2^{ - 10}\) | 0.4102 | 0.6472 | 1.1238 | 0.9623 |
\(2^{ - 12}\) | 0.7550 | 0.6966 | 0.6544 | 0.9477 |
\(2^{ - 18}\) | 0.2844 | 0.6496 | 0.6469 | 0.8100 |