Runge–Kutta method
This online calculator implements Runge-Kutta method, which is a fourth-order numerical method to solve first degree differential equation with a given initial value.
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Runge–Kutta method
Digits after the decimal point: 2
Differential equation
y′=y
Approximate value of y
2.72
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Approximation
| n | x{n} | y{n} | k1 | k2 | k3 | k4 | y{n+1} |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0.1 | 0.11 | 0.11 | 0.11 | 1.11 |
| 1 | 0.1 | 1.11 | 0.11 | 0.12 | 0.12 | 0.12 | 1.22 |
| 2 | 0.2 | 1.22 | 0.12 | 0.13 | 0.13 | 0.13 | 1.35 |
| 3 | 0.30 | 1.35 | 0.13 | 0.14 | 0.14 | 0.15 | 1.49 |
| 4 | 0.4 | 1.49 | 0.15 | 0.16 | 0.16 | 0.16 | 1.65 |
| 5 | 0.5 | 1.65 | 0.16 | 0.17 | 0.17 | 0.18 | 1.82 |
| 6 | 0.6 | 1.82 | 0.18 | 0.19 | 0.19 | 0.20 | 2.01 |
| 7 | 0.7 | 2.01 | 0.20 | 0.21 | 0.21 | 0.22 | 2.23 |
| 8 | 0.80 | 2.23 | 0.22 | 0.23 | 0.23 | 0.25 | 2.46 |
| 9 | 0.90 | 2.46 | 0.25 | 0.26 | 0.26 | 0.27 | 2.72 |
| 10 | 1.00 | 2.72 | |||||
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