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Unformatted text preview: smaller than necessary? Answer: We know that if our old values are correct, y ab n +1-y ( t n +1 ) = 3 h 4 8 y (4) ( η ) . y am n +1-y ( t n +1 ) =-h 4 24 y (4) ( ν ) . Subtracting, we obtain y ab n +1-y am n +1 = 3 h 4 8 y (4) ( η )-(-h 4 24 y (4) ( ν )) where η, ν are in the interval containing y ab n +1 , y am n +1 , and the true value. Since 3 / 8+1 / 24 = 10 / 24, the error in AM can be estimated as ² = | y ab n +1-y am n +1 | / 10. Now, if ² > τ , we might reduce h by a factor of 2 and retake the step. If ² << τ , we might double h in preparation for the next step (expecting that the local error might increase by a factor of 2 4 ). 2...
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- Fall '06
- Hamiltonian mechanics, Hamiltonian, Symplectic manifold, Symplectic geometry, local error