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

Predict higpa using a logistic regression, In this problem, we use the CSDA...

In this problem, we use the CSDATA data set, which is available in 'CSDATA.txt'. We do ne an indicator variable, say HIGPA, to be 1 if the GPA is 3.0 or better and 0 other- wise. S

Team Collaboration: Business Decision Making Project, Collect data about th...

Collect data about the chosen business problem or opportunity at the company. Explain how you obtained a suitable sample of either qualitative or quantitative data. Review data f

Assumptions in anova, Assumptions in ANOVA The various populations f...

Assumptions in ANOVA The various populations from which the samples are drawn should be normal and have the same variance. The requirement of normality can be discarded if t

Diversity of data , The box plot displays the diversity of data for the tot...

The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.

Types of cost-reimbursable contracts, Types of cost-reimbursable contracts ...

Types of cost-reimbursable contracts are:   Cost Plus Fixed Fee contract (CPPF): Compensation is based on a fixed sum independent of the final project cost. The customer a

Time series, Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 ...

Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 2012 14 2013 16 Determine the trend from data given above?

Mathematical properties of arithmetic mean, Mathematical Properties ...

Mathematical Properties The sum of deviations of the items from the arithmetic mean (taking signs into account) is always zero, i.e.      = 0. The sum of

Evaluate the standard deviation, Use only the rare event rule, and make sub...

Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consis

Probability, .1 Modern hotels and certain establishments make use of an ele...

.1 Modern hotels and certain establishments make use of an electronic door lock system. To open a door an electronic card is inserted into a slot. A green light indicates that the

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