Skip to main content

Table 2 Absolute errors for Example 1 given by \(\Vert y_e-y_a\Vert\)

From: An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration

t \(m=2\) \(m=3\) \(m=5\) \(m=7\) \(m=9\)
0.0 7.91342855 \(\times 10^{-2}\) 8.67203112 \(\times 10^{-2}\) 1.7122077 \(\times 10^{-3}\) 1.36462 \(\times 10^{-5}\) 9.350\(\times 10^{-7}\)
0.1 1.488264874 \(\times 10^{-1}\) 1.99981028 \(\times 10^{-2}\) 5.938054 \(\times 10^{-4}\) 2.8730 \(\times 10^{-6}\) 2.862\(\times 10^{-7}\)
0.2 1.315948258 \(\times 10^{-1}\) 4.17514750 \(\times 10^{-2}\) 4.789498 \(\times 10^{-4}\) 5.7607\(\times 10^{-6}\) 2.362\(\times 10^{-7}\)
0.3 6.77587069\(\times 10^{-2}\) 1.88592116 \(\times 10^{-2}\) 3.553027 \(\times 10^{-4}\) 3.5319 \(\times 10^{-6}\) 9.92\(\times 10^{-8}\)
0.4 9.8506587 \(\times 10^{-3}\) 1.58474766 \(\times 10^{-2}\) 3.899000 \(\times 10^{-4}\) 4.1422 \(\times 10^{-6}\) 1.205\(\times 10^{-7}\)
0.5 7.90561751 \(\times 10^{-2}\) 4.01914937 \(\times 10^{-2}\) 5.036652 \(\times 10^{-4}\) 4.9631\(\times 10^{-6}\) 2.401\(\times 10^{-7}\)
0.6 1.288352991\(\times 10^{-1}\) 4.31502967 \(\times 10^{-2}\) 1.387573 \(\times 10^{-4}\) 2.8589 \(\times 10^{-6}\) 1.303\(\times 10^{-7}\)
0.7 1.579359764\(\times 10^{-1}\) 2.34718312 \(\times 10^{-2}\) 6.119877 \(\times 10^{-4}\) 5.8336 \(\times 10^{-6}\) 8.99\(\times 10^{-8}\)
0.8 1.724335492 \(\times 10^{-1}\) 1.27685605 \(\times 10^{-2}\) 7.76566 \(\times 10^{-5}\) 9.540\(\times 10^{-7}\) 2.330\(\times 10^{-7}\)
0.9 1.829509214\(\times 10^{-1}\) 5.49479747 \(\times 10^{-2}\) 7.417110 \(\times 10^{-4}\) 2.7400 \(\times 10^{-6}\) 2.851\(\times 10^{-7}\)
1.0 2.020789096 \(\times 10^{-1}\) 9.04755948 \(\times 10^{-2}\) 1.7110015 \(\times 10^{-3}\) 1.36480 \(\times 10^{-5}\) 9.350\(\times 10^{-7}\)