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There was a sign error in Adams-Basforth coefficient (Remember that the sum of these coefficient must equal 1 :)) |
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y_{n+1} &= y_n + hf(t_n, y_n) , \qquad\text{(This is the Euler method)} \\
y_{n+2} &= y_{n+1} + h\left( \frac{3}{2}f(t_{n+1}, y_{n+1}) - \frac{1}{2}f(t_n, y_n) \right) , \\
y_{n+3} &= y_{n+2} + h\left( \frac{23}{12} f(t_{n+2}, y_{n+2}) - \frac{4}{3} f(t_{n+1}, y_{n+1})
y_{n+4} &= y_{n+3} + h\left( \frac{55}{24} f(t_{n+3}, y_{n+3}) - \frac{59}{24} f(t_{n+2}, y_{n+2}) + \frac{37}{24} f(t_{n+1}, y_{n+1}) - \frac{3}{8} f(t_n, y_n) \right) , \\
y_{n+5} &= y_{n+4} + h\left( \frac{1901}{720} f(t_{n+4}, y_{n+4}) - \frac{1387}{360} f(t_{n+3}, y_{n+3}) + \frac{109}{30} f(t_{n+2}, y_{n+2}) - \frac{637}{360} f(t_{n+1}, y_{n+1}) + \frac{251}{720} f(t_n, y_n) \right) .
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