Midpoint method
This online calculator implements explicit midpoint method AKA modified Euler method, which is a second order numerical method to solve first degree differential equation with a given initial value.
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Articles that describe this calculator
Midpoint method
Digits after the decimal point: 2
Differential equation
y′=y
Approximate value of y
2.71
Approximation
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Approximation
Exact solution
Approximation
| n | x{n} | Approximation | f(x,y) | dy | y{n+1} | Exact solution | Absolute error |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0.11 | 1.10 | 1 | 0 |
| 1 | 0.1 | 1.10 | 1.10 | 0.12 | 1.22 | 1.11 | 0.0002 |
| 2 | 0.2 | 1.22 | 1.22 | 0.13 | 1.35 | 1.22 | 0.0004 |
| 3 | 0.30 | 1.35 | 1.35 | 0.14 | 1.49 | 1.35 | 0.0006 |
| 4 | 0.4 | 1.49 | 1.49 | 0.16 | 1.65 | 1.49 | 0.0009 |
| 5 | 0.5 | 1.65 | 1.65 | 0.17 | 1.82 | 1.65 | 0.0013 |
| 6 | 0.6 | 1.82 | 1.82 | 0.19 | 2.01 | 1.82 | 0.0017 |
| 7 | 0.7 | 2.01 | 2.01 | 0.21 | 2.22 | 2.01 | 0.0022 |
| 8 | 0.80 | 2.22 | 2.22 | 0.23 | 2.46 | 2.23 | 0.0028 |
| 9 | 0.90 | 2.46 | 2.46 | 0.26 | 2.71 | 2.46 | 0.0034 |
| 10 | 1.00 | 2.71 | 2.72 | 0.0042 | |||
Calculators used by this calculator
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#differentiation #midpoint differentiation Euler Math Midpoint method modified Euler method Numerical differential equations
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