Iterative convergence of the method, Applied Statistics

Assignment Help:

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:

588_Iterative convergence of the method.png

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.


Related Discussions:- Iterative convergence of the method

Bernoulli trial, Statistician is searching the \home ground" effect and is ...

Statistician is searching the \home ground" effect and is studying 20 football games, of which 14 were won by the home team and 6 by the visitors. Therefore the game is a Bernoulli

Che, Chebychev inequality

Chebychev inequality

Break-even analysis, a. How can break-even analysis be used in selecting a ...

a. How can break-even analysis be used in selecting a new plant site? b. What are potential advantages and disadvantage of locating a production facility in foreign country i

Quantitative Models, Consider the following new business venture. An agent ...

Consider the following new business venture. An agent is considering investment in one of three real estate parcels: • Option 1: multiunit rentals • Option 2: commercial building

Large sample test for mean, Large Sample Test for Mean A random sample ...

Large Sample Test for Mean A random sample of size n (n > 30) has a sample mean    . To test the hypothesis that the population mean μ has a specified value  μ 0  let us formu

Evaluate minimum capability requirement, You are currently working wit...

You are currently working with a supplier who is producing a shaft whose diameter specification is 6.00 ± .003 inches.  Currently, the process is yielding shafts wit

Multiple regressions, A sample of 43 houses that were purchased in the Sout...

A sample of 43 houses that were purchased in the Southern California town Monrovia within a month was collected. We are interested in the study of the relationships between Price a

Statistical process control, Statistical Process Control The variabilit...

Statistical Process Control The variability present in manufacturing process can either be eliminated completely or minimized to the extent possible. Eliminating the variabilit

Canonical correlation analysis, Canonical correlation analysis (CC) allows ...

Canonical correlation analysis (CC) allows the investigation of the relationship between two ,sets of variables. For example, a sociologist may want to investigate the Relationship

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd