| 1 |
Runge Kutta methods achieve better results than Euler by using intermediate computations at intermediate time values
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| 2 |
The fourth-order rule is the favorite method as it achieves good accuracy with modest computational complexity -- the algorithm is in words:
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| 3 |
Use derivative of first time step to get trial midpoint
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| 4 |
Use its derivative at first time step to get second trial midpoint
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| 5 |
Use its derivative to get a trial end point
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| 6 |
Integrate by Simpon's Rule, using average of two midpoint estimates
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| 7 |
Global error is fourth order
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