Explicit Runge–Kutta methods
This online calculator implements several explicit Runge-Kutta methods so you can compare how they solve first degree differential equation with a given initial value.
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Explicit Runge–Kutta methods
Digits after the decimal point: 6
Differential equation
y′=y
Exact solution
2.718282
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Methods
| Method name | Approximate solution | Error |
|---|---|---|
| Forward Euler | 2.593742 | 0.124539 |
| Explicit midpoint method | 2.714081 | 0.004201 |
| Heun's method | 2.714081 | 0.004201 |
| Ralston's method | 2.714081 | 0.004201 |
| Kutta's third-order method | 2.718177 | 0.000105 |
| Heun's third-order method | 2.718177 | 0.000105 |
| Ralston's third-order method | 2.718177 | 0.000105 |
| Third-order Strong Stability Preserving Runge-Kutta (SSPRK3) | 2.718177 | 0.000105 |
| Classic fourth-order method | 2.718280 | 0.000002 |
| Ralston's fourth-order method | 2.718280 | 0.000002 |
| 3/8-rule fourth-order method | 2.718280 | 0.000002 |
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#differentiation #Runge-Kutta 3/8-rule fourth-order method Classic fourth-order method differentiation Explicit midpoint method Forward Euler Heun's method Heun's third-order method Kutta's third-order method Math Numerical differential equations Ralston's fourth-order method Ralston's method Ralston's third-order method Third-order Strong Stability Preserving Runge-Kutta (SSPRK3)
PLANETCALC, Explicit Runge–Kutta methods
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