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

Riemannian integral approximations, Investigate the use of fixed and perce...

Investigate the use of fixed and percentile meshes when applying chi squared goodness-of- t hypothesis tests. Apply the oversmoothing procedure to the LRL data. Compare the res

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

Importance and application of probability, Importance and Application of pr...

Importance and Application of probability: Importance of probability theory  is in all those areas where event are not  certain to take place as same  as starting with games of

Determine market interest rate, The interest rate on the three year loan is...

The interest rate on the three year loan is 0.087. Whereas the interest rate on the two year loan is 0.085 as given in A. Suppose that the liquidity premium at t=1 is 0.002 and tha

Calculate mean and standard deviation, Select and generate your assignment ...

Select and generate your assignment portfolio. The S&P/ASX 200 index is comprised of several sub-indices, including the following: 0) XPJ: The S&P/ASX 200 A-REIT Index 1) XDJ

Introduction to multiple regression, In simple regression the dependent var...

In simple regression the dependent variable Y was assumed to be linearly related to a single variable X. In real life, however, we often find that a dependent variable may depend o

Find probability of remaining paint free - ball duel, In a three-cornered p...

In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. Once hit, a player is out of the game and gets no

LINEAR PROGRAMMING FOR SOLVNG INEQUALITIES, To use Linear Programming for s...

To use Linear Programming for solving the following inequalities. Following Twin Conditions (as mandated by the Indian Regulatory Authority) Twin Condition I for TV Broadcasters

Critique 2, prepare a critical analysis of a quantitative study focusing on...

prepare a critical analysis of a quantitative study focusing on protection of human participants data collection data management and analysis problem statement and interpretation o

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