assign10-09

# assign10-09 - y n +1 = y n + 1-1 2 a k 1 + 1 2 a k 2 ,...

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MATH 573 ASSIGNMENT 10 1. Determine the interval of absolute stability for the method: y n +1 = y n + h 2 [3 f n - f n - 1 ] . 2. Determine the interval of relative stability for the method of problem 1. The interval of absolute stability can be deﬁned more generally as those values of λh for which all solutions of an approximation scheme remain bounded when applied to the model problem y 0 = λy . Use this deﬁnition in the following two problems. 3. Find the interval of absolute stability for the general R-K method of order 2, i.e.,
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Unformatted text preview: y n +1 = y n + 1-1 2 a k 1 + 1 2 a k 2 , where k 1 = hf ( x n , y n ) , k 2 = hf ( x n + ah, y n + ak 1 ) . 4. Find the interval of absolute stability for the method consisting of one application of the corrector y n +1 = y n + h 2 [ f ( x n +1 , y n +1 ) + f ( x n , y n )] after the predictor y n +1 = y n + hf ( x n , y n ) . 1...
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## This note was uploaded on 10/16/2010 for the course MATH FIN 621 taught by Professor Paulfeehan during the Spring '09 term at Rutgers.

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