GDB solution of mth603 last date July 09, 2012 to July 11, 2012

[DuAa RaNi!]

Graded MDB

Dated: Jul 05, 12

Dear Students,   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.”   Instructions:  (1) Post your comments on Graded MDB & not on Regular Lecture MDB.  (2) Do not use the symbols of math type and avoid figures.  (3) Zero marks will be given to Copied or Irrelevant comments.  (4) The comments should be clear and to the point.  (5) No extra time will be given for discussion.  (6) You can not participate in the discussion after due date or through        e-mail.   (7) Properly prepare yourself about the topic using books or any source     available to you. (8) The remarks about the topic should be your own struggle from books, literature articles and internet and not be same as it.

[DuAa RaNi!]

idea solution

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 predictor-corrector 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

[+ M.Tariq Malik]

dua gee..*_*  gud keep it up 

[DuAa RaNi!]

thanks tariq bhiaaa

[DuAa RaNi!]

welcm sis 

[+ M.Tariq Malik]

Please Discuss here about this GDB.thanks

[+ M.Tariq Malik]

ji bayata ji 

[+ M.Tariq Malik]

Nabila ch hmm gud 

[+ M.Tariq Malik]

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).

[DuAa RaNi!]

add more idea plzzz

[+ M.Tariq Malik]

1. The P-C methods may provide both high accuracy and the capability of error monitoring,all at a potentially lower computational cost than RK-Fehlberg or RK-Merson methods.For example, the Adams-Moulton 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 Adam-Moulton requires fewer function evaluations than either RK-Merson or RK-Fehlberg
2. The adjustment of the step size in P-C 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 Adams-Bashforth method (whichwould reduce the global error by a factor of 24 = 16, i.e. a lot) and then use it alonewithout the Adams-Moulton corrector formula? The answer is this. First, one willthen lose the ability to monitor the error. Second, the Adams-Bashforth may sometimesproduce a numerical solution which has nothing to do with the exact solution, whilethe P-C Adams-Moulton's solution will stay close to the exact one.

[+ M.Tariq Malik]

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