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

Quartiles, Related Positional Measures Besides median, there are other ...

Related Positional Measures Besides median, there are other measures which divide a series into equal parts. Important amongst these are quartiles, deciles and percentiles.

Concepts of statistics, what are the importance, uses,optimums and applicat...

what are the importance, uses,optimums and applications of the following in agriculture field experiments; 1.standard deviation 2.standard error 3. coefficient of variation

Philosophy, what is the aim of statistics?

what is the aim of statistics?

Determine relative frequency, A sample of college students and a separate s...

A sample of college students and a separate sample of adults aged 30-59 were surveyed regarding the amount of fruit they eat each day.  The results are shown in the histograms belo

., differance b/w big M mathod and two phase mathod

differance b/w big M mathod and two phase mathod

Empirical mode, Empirical Mode Where mode is ill-defined, its value may...

Empirical Mode Where mode is ill-defined, its value may be ascertained by the following formula based upon the empirical relationship between Mean, Median and Mode: Mode = 3

Regression, The 4 assumptions of regression: 1.       Variables are norm...

The 4 assumptions of regression: 1.       Variables are normally distributed 2.       Linear relationship between the independent and dependent variables 3.       Homosced

Calculate unbiased estimate of the variance, This question has two parts wi...

This question has two parts with multiple items to answer. You are a psychologist who has collected the subjective well-being scores of a number of elderly people aged 90 or abo

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