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

Plot diagnostic quantities, The data in the data frame compensation are fro...

The data in the data frame compensation are from Myers (1990), Classical andModern Regression with Applications (Second Edition)," Duxbury. The response y here is executive compens

Harmonic mean, The Harmonic Mean is based on the reciprocals of numbers ave...

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th

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

Determine the maximum weight rounded down, Assume that the pulley at A is a...

Assume that the pulley at A is a small frictionless pulley. The cord AB is only allowed to support a maximum tension in Newtons as given in P4, and the cord supporting the block ca

Correlation coefficient test, 1. If you are calculating a correlation coeff...

1. If you are calculating a correlation coefficient testing the relationship between height and weight, state the null and alternative hypotheses. 2. What kind of relationship d

Three types of food question?, #There were three types of food, and the res...

#There were three types of food, and the researcher recorded which foods were bought. Peanut Butter Banana Hamburger 15

Graphical calculation for mode, For calculating the mode of the grouped dat...

For calculating the mode of the grouped data graphically, the following procedure is adopted. Draw a histogram of the data; the modal class is the tallest rectangle.

Difference in goals between pca and fa, In PCA the eigknvalues must ultimat...

In PCA the eigknvalues must ultimately account for all of the variance. There is no probability,'no hypothesis, no test because strictly speaking PCA is not a statistical procedure

Deviation measures, Deviation Measures The drawback of the range as a m...

Deviation Measures The drawback of the range as a measure of dispersion is that it takes into account the values of only two data points - the largest and the smallest. One

Chi square test as a distributional goodness of fit, Chi Square Test as a D...

Chi Square Test as a Distributional Goodness of Fit In day-to-day decision making managers often come across situations wherein they are in a state of dilemma about the applica

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