Comparing Numerical Methods for Differential Equations
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Why the 3-step Adams Moulton method is better than the 2-step Adams Moulton method?
Noted that the local truncation error of 3-step Adams Moulton method is $O(h^4)$, while the local truncation error of 2-step Adams Moulton method is $O(h^3)$.
Are there other reasons or tools to compare between two previous numerical methods, e.g. factors and measures that need to be studied like computational cost, efficiency, convergence, simplicity and other factors that might be proper to determine which method is better.
convergence numerical-methods truncation-error
asked Sep 1 at 1:23
workwolf
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up vote
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Why the 3-step Adams Moulton method is better than the 2-step Adams Moulton method?
Noted that the local truncation error of 3-step Adams Moulton method is $O(h^4)$, while the local truncation error of 2-step Adams Moulton method is $O(h^3)$.
Are there other reasons or tools to compare between two previous numerical methods, e.g. factors and measures that need to be studied like computational cost, efficiency, convergence, simplicity and other factors that might be proper to determine which method is better.
convergence numerical-methods truncation-error
asked Sep 1 at 1:23
workwolf
84
Order of accuracy, stability, and computational cost are the three main criteria on which numerical methods are evaluated. Another might be conservation of invariants, for example one might prefer symplectic methods for Hamiltonian systems since they approximately preserve the energy of the system.
– Rahul
Sep 1 at 3:21
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Why the 3-step Adams Moulton method is better than the 2-step Adams Moulton method?
Noted that the local truncation error of 3-step Adams Moulton method is $O(h^4)$, while the local truncation error of 2-step Adams Moulton method is $O(h^3)$.
Are there other reasons or tools to compare between two previous numerical methods, e.g. factors and measures that need to be studied like computational cost, efficiency, convergence, simplicity and other factors that might be proper to determine which method is better.
convergence numerical-methods truncation-error
asked Sep 1 at 1:23
workwolf
84
Why the 3-step Adams Moulton method is better than the 2-step Adams Moulton method?
Noted that the local truncation error of 3-step Adams Moulton method is $O(h^4)$, while the local truncation error of 2-step Adams Moulton method is $O(h^3)$.
Are there other reasons or tools to compare between two previous numerical methods, e.g. factors and measures that need to be studied like computational cost, efficiency, convergence, simplicity and other factors that might be proper to determine which method is better.
convergence numerical-methods truncation-error
convergence numerical-methods truncation-error
asked Sep 1 at 1:23
workwolf
84
asked Sep 1 at 1:23
workwolf
84
edited Sep 1 at 2:15
asked Sep 1 at 1:23
workwolf
84
asked Sep 1 at 1:23
workwolf
84
asked Sep 1 at 1:23
workwolf
84
84
Order of accuracy, stability, and computational cost are the three main criteria on which numerical methods are evaluated. Another might be conservation of invariants, for example one might prefer symplectic methods for Hamiltonian systems since they approximately preserve the energy of the system.
– Rahul
Sep 1 at 3:21
add a comment |Â
Order of accuracy, stability, and computational cost are the three main criteria on which numerical methods are evaluated. Another might be conservation of invariants, for example one might prefer symplectic methods for Hamiltonian systems since they approximately preserve the energy of the system.
– Rahul
Sep 1 at 3:21
Order of accuracy, stability, and computational cost are the three main criteria on which numerical methods are evaluated. Another might be conservation of invariants, for example one might prefer symplectic methods for Hamiltonian systems since they approximately preserve the energy of the system.
– Rahul
Sep 1 at 3:21
Order of accuracy, stability, and computational cost are the three main criteria on which numerical methods are evaluated. Another might be conservation of invariants, for example one might prefer symplectic methods for Hamiltonian systems since they approximately preserve the energy of the system.
– Rahul
Sep 1 at 3:21
add a comment |Â
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Order of accuracy, stability, and computational cost are the three main criteria on which numerical methods are evaluated. Another might be conservation of invariants, for example one might prefer symplectic methods for Hamiltonian systems since they approximately preserve the energy of the system.
– Rahul
Sep 1 at 3:21