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

Demand, A monopolist firm''s demand curve is given by P:100-2q. (a) Find it...

A monopolist firm''s demand curve is given by P:100-2q. (a) Find its marginal revenue function.

Prediction interval, Prediction Inte rval We would like to construct a...

Prediction Inte rval We would like to construct a prediction interval around    which would contain the actual Y. If n  ≥  30,     ± Zs e  would be the interval, where Z

Statistical quality control assinment, how to get statistical quality contr...

how to get statistical quality control assignment in brief?

Compute the standard deviation, Let X, Y, and Z refer to the three random v...

Let X, Y, and Z refer to the three random variables. It is known that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermor

Data analysis, #quesgraphical representation of data

#quesgraphical representation of data

Sensitivity and Specificity tests, The prevalence of undetected diabetes in...

The prevalence of undetected diabetes in a population to be screened is approximately 1.5% and it is assumed that 10,000 persons will be screened. The screening test will measure

Continuous frequency distribution, Formation of Continuous Frequency Distri...

Formation of Continuous Frequency Distribution:    Continuous frequency distribution is most popular in practice. With reference to the formation of this type of frequency distr

the npv of the book , Bill Clinton reportedly was paid $10 million to writ...

Bill Clinton reportedly was paid $10 million to write his book My Way. The book took three years to write. In the time he spent writing, Clinton could have been paid to make speech

Regression coefficient, Regression Coefficient While analysing regressi...

Regression Coefficient While analysing regression in two related series, we calculate their regression coefficients also. There are two regression coefficients like two regress

Multiple correspondence analysis, Correspondence analysis is an exploratory...

Correspondence analysis is an exploratory technique used to analyze simple two-way and multi-way tables containing measures of correspondence between the rows and colulnns of an

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