\(t\) | Value of (x) | Numerical solution | Exact solution | Abs error |
---|---|---|---|---|
\(t = 0\) | 0 | 1 | 1 | 0 |
2 | − 0.4161468365 | − 0.4161468365 | 0 | |
4 | − 0.6536436209 | − 0.6536436209 | 0 | |
6 | 0.9601702867 | 0.9601702867 | 0 | |
8 | − 0.1455000338 | − 0.1455000338 | 0 | |
10 | − 0.8390715291 | − 0.8390715291 | 0 | |
\(t = 1\) | 0 | 0.5403023059 | 0.5403023059 | \({3}{\text{.186028260 }} \times 10^{ - 11}\) |
2 | 0.5403023057 | 0.5403023059 | \({2 } \times 10^{ - 10}\) | |
4 | − 0.9899924967 | − 0.9899924966 | \({1} \times 10^{ - 10}\) | |
6 | 0.2836621855 | 0.2836621855 | 0 | |
8 | 0.7539022544 | 0.7539022543 | \({1} \times 10^{ - 10}\) | |
10 | − 0.9111302620 | 0.9111302619 | \({1} \times 10^{ - 10}\) | |
\(t = 2\) | 0 | − 0.4161468396 | − 0.4161468365 | \({3}{\text{.05285761300}} \times 10^{ - 9}\) |
2 | 1.000000023 | 1 | \({2}{\text{.3 }} \times 10^{ - 8}\) | |
4 | − 0.4161468534 | − 0.4161468365 | \({1}{\text{.69 }} \times 10^{ - 8}\) | |
6 | − 0.6536436313 | − 0.6536436209 | \({1}{\text{.04 }} \times 10^{ - 8}\) | |
8 | 0.9601703110 | 0.9601702867 | \({2}{\text{.43 }} \times 10^{ - 8}\) | |
10 | − 0.1455000450 | − 0.1455000338 | \({1}{\text{.12 }} \times 10^{ - 8}\) | |
\(t = 3\) | 0 | − 0.9899944948 | − 0.9899924966 | \(1.9982 \times 10^{ - 6}\) |
2 | 0.5403127921 | 0.5403023059 | \({104862} \times 10^{ - 5}\) | |
4 | 0.5402955751 | 0.5403023059 | \({6}{\text{.7308}} \times 10^{ - 6}\) | |
6 | − 0.9899973839 | 0.9899924966 | \({4}{\text{.8873}} \times 10^{ - 6}\) | |
8 | 0.2836729814 | 0.2836621855 | \({1}.07959 \times 10^{ - 5}\) | |
10 | 0.7538981557 | 0.7539022543 | \(4.0986 \times 10^{ - 6}\) |