Iterative convergence of the method, Applied Statistics

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.

Posted Date: 3/8/2013 12:31:31 AM | Location : United States







Related Discussions:- Iterative convergence of the method, Assignment Help, Ask Question on Iterative convergence of the method, Get Answer, Expert's Help, Iterative convergence of the method Discussions

Write discussion on Iterative convergence of the method
Your posts are moderated
Related Questions

Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coi

Consider the linear transformation (a) Find the image of (3 , -2 , 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transf

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

A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies

(1) Assume we categorize voters in a city as havingless educationand those havingmoreeducation. Those with less education have less than a college degree; those with more education

In an examination 600 candidates appeared, boys outnumbered girls by 16% of all candidates. number of passed candidates exceeded the number of failed candidates by 310. Boys failin


In reduced rank regression (RRR), the dependent variables are first submitted to a PCA and the scores of the units are then used as dependent variables in a series of

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