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Graded MDB  Dated: Jul 05, 12 
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A Graded MDB will be opened on Tuesday July 09, 2012 at 12:01 AM This discussion board will be closed on July 11, 2012 at 11:59 PM It is necessary for every student to take part in this discussion board. Your comments will be graded, which is worth 5% of your total marks. You should remember that you have to post your comments about the discussion title with in the time as mentioned above.
The topic for Graded Moderated Discussion Board is
“Compare the efficiency and characteristics of Predictor Corrector methods available to you.”
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Predictor–corrector method is an algorithm thatproceeds in two steps. First, the prediction step calculates a roughapproximation of the desired quantity. Second, the corrector step refines theinitial approximation using another means. A predictor–corrector methodtypically uses an explicit method for the predictor step and animplicit method for the corrector step. A simple predictor–corrector method canbe constructed from the Eulermethod (an explicit method) and the trapezoidal rule (an implicit method).
Effectivenessand Characteristics
The idea behind the predictorcorrector methods is to use asuitable combination of an explicit and an implicit technique to obtain amethod with better convergence characteristics Runge Kutta method Euler Method, Trapezoidal Rule arepredictor corrector methods
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Please Discuss here about this GDB.thanks
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Predictor–corrector method is an algorithm thatproceeds in two steps. First, the prediction step calculates a roughapproximation of the desired quantity. Second, the corrector step refines theinitial approximation using another means. A predictor–corrector methodtypically uses an explicit method for the predictor step and animplicit method for the corrector step. A simple predictor–corrector method canbe constructed from the Eulermethod (an explicit method) and the trapezoidal rule (an implicit method).
add more idea plzzz
1. The PC methods may provide both high accuracy and the capability of error monitoring,all at a potentially lower computational cost than RKFehlberg or RKMerson methods.For example, the AdamsMoulton method (3.34) has the error of the same (fourth) orderas the aforementioned RK methods, while requiring k + 1 function evaluations, where kis the number of times one has to iterate the corrector equation. If k < 4, then AdamMoulton requires fewer function evaluations than either RKMerson or RKFehlberg
2. The adjustment of the step size in PC methods is awkward (as it is in all multistepmethods); see the end of Sec. 3.1 and Remark 3 above.
3. One may ask, why not just halve the step size of the AdamsBashforth method (whichwould reduce the global error by a factor of 24 = 16, i.e. a lot) and then use it alonewithout the AdamsMoulton corrector formula? The answer is this. First, one willthen lose the ability to monitor the error. Second, the AdamsBashforth may sometimesproduce a numerical solution which has nothing to do with the exact solution, whilethe PC AdamsMoulton's solution will stay close to the exact one.
for more information check this link plz..........
http://books.google.com.pk/books?id=hXQu7toVYjQC&pg=PA381&d... +for+ode&hl=en&sa=X&ei=97z4T
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