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

Express the null hypothesis, Examine the given statement, then express the ...

Examine the given statement, then express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. The mean weight of women who won a beauty pageant is equal t

Index Number of formulae, discuss the mathematical test of adequacy of inde...

discuss the mathematical test of adequacy of index number of formulae. prove algebraically that the laspeyre, paasche and fisher price index formulae satisfies this test. What is

Types of business forecasting , Types  of business forecasting  are genera...

Types  of business forecasting  are generally as follows: 1.      Sales  and Demand  forecasts 2.      Porduction  forecasts. 3.       Cost  Forecasts 4.       Financi

Find the unbiased estimators for mean and variance matrix, Is the random ve...

Is the random vector (Trunk Space, Length, Turning diameter) of US car normally distributed? Why? If yes, find the unbiased estimators for the mean and variance matrix of (Trunk Sp

What is the p-value, Use the information given below to find the P-value. ...

Use the information given below to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to

Non-sampling errors, Statistics Can Lead to Errors The use of st...

Statistics Can Lead to Errors The use of statistics can often lead to wrong conclusions or wrong estimates. For example, we may want to find out the average savings by i

Show a simple linear regression analysis, In the early 1990s researchers at...

In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and Wh

Asymmetric proximity matrices, Asymmetric proximity matrices Immediacy...

Asymmetric proximity matrices Immediacy matrices in which the off-diagonal elements which are, in the i th row and j th column and the j th row and i th column, are not essent

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