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You are given the differential equation dy/dx = y' = f(x, y) with initial condition y(0 ) 1 = . The following numerical method is also given:
where fn = f( xn , yn) = f(nh, yn) x , y f nh, y = = and h is the integration step.
(a) Is this an explicit or implicit method? Explain you answer.
(b) Find an expression for local error of this method.
(c) If one takes f = - σy (where σ > 0 and constant) is this method stable? Prove your answer mathematically.
(d) What is the condition for the iterative convergence of the method (when f = - σy )? Show that fulfillment of the condition for stability of the method assures iterative convergence.
1. Recognize and explain the opportunities for statistical learning. 2. Describe how the use of statistics supports student learning. 3. Recognize appropriate data displays a
mark number of student 0-10 4 10-20 8 20-30 11 30-40 15 40-50 12 50-60 6 calculate frequency distribution
prove standard deviation of natural natural numbers
Median Median is a position average. It is the value of middle item of a variable when the items are arranged according to their values either in ascending or descending order.
The interest rate on the three year loan is 0.087. Whereas the interest rate on the two year loan is 0.085 as given in A. Suppose that the liquidity premium at t=1 is 0.002 and tha
Characteristics of Index Number On the analysis of various definitions of index number the following may be its characteristics: 1. Expressed in Number : Index number
Old Faithful Geyser in Yellowstone National Park derives its names and fame from the regularity (and beauty) of its eruptions. Rangers usually post the predicted times of eruptions
Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 2012 14 2013 16 Determine the trend from data given above?
Henry Kaiser suggested a rule for selecting a number of components m less than the number needed for perfect reconstruction: set m equal to the number of eigenvalues greater than I
Central Tendency and Dispersion in Statistics: Write a note on the following : i) What is the importance of Measures Of Central Tendency and Dispersion in Statistics ?
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