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

Correlation, Correlation The correlation is commonly used and a useful...

Correlation The correlation is commonly used and a useful statistic used to describe the degree of the relationships between two or more variables. Pearson's correlation refle

Business forecasting, Meaning and Definitions of Business Forecasting T...

Meaning and Definitions of Business Forecasting The problem of business  forecasting  refers to the  analysis  of the past and  present economic  conditions. With  the objectiv

Probability, Ask queFrom these studies, which of the following may be consi...

Ask queFrom these studies, which of the following may be considered a variable that can have a probability distribution? [I] Percentage of Sub-Saharan Africans that smoke [II] Perc

PERCENTAGES, CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 U...

CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 UNDER THE CURRENT WITHHOLDING GUIDELINES

Recitilinear motion, velocity of a particle which moves along the s-axis is...

velocity of a particle which moves along the s-axis is given by v=2-4t+5t then find position velocity,acceleration

What is the probability that they all hit the target, QUESTION ONE. (a) ...

QUESTION ONE. (a) The probability that, a bomber hits a target on a bombing mission is 0.70 Three bombers are sent to bomb a particular target. (i) What is the probability

Linear regression mode, The State Department of Taxation wishes to investig...

The State Department of Taxation wishes to investigate the effect of experience, x, on the amount of time, y, required to fill out Form ST 1040AVG, the state income-averaging form.

Question with R - Bioinformatics, Hi There, I have a question regarding R,...

Hi There, I have a question regarding R, and I am wondering if anyone can help me. Here is a code that I would like to understand: squareFunc g f(x)^2 } return(g) } sin

Decision making ., it is said that management is equivalent to decision mak...

it is said that management is equivalent to decision making? do you agree? explain

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