Theorem of continuous functions, Mathematics

Assignment Help:

Consider the subsequent IVP.

y' = f(t,y) ,        y(t0) = y0

If f(t,y) and ∂f/∂y are continuous functions in several rectangle a < t < b, g < y  < d, containing the point  (to, yo) then there is a unique solution to the IVP in some interval to - h < t < to + h which is included in a < t < b.

That's it.  Unlike the first theorem, this one cannot really be used to find an interval of validity. Thus, we will know that a unique solution exists if the conditions of the theorem are met, but we will in fact need the solution in order to find out its interval of validity.  Remember as well that for non-linear differential equations it emerges that the value of y0 may influence the interval of validity.

Here is an illustration of the problems that can happen when the conditions of this theorem are not met.


Related Discussions:- Theorem of continuous functions

Matrices, find inverse of [1 2 3 2 4 5 3 5 6]

find inverse of [1 2 3 2 4 5 3 5 6]

Marketing mix, 1) Identify key characteristics of product or services and e...

1) Identify key characteristics of product or services and estimate their significance to the market 2) Identify and analyse level of customer service provision to determine its si

What is the conditional probability based on die questions, A die is rolled...

A die is rolled twice and the sum of the numbers appearing on them is observed to be 7.What is the conditional probability that the number 2 has appeared at least once? A) 1/3

What is place value?, WHAT IS PLACE VALUE? : (This section is only for you...

WHAT IS PLACE VALUE? : (This section is only for your assumptions, and not-meant to be passed on to your learners.) You may have realised that in the decimal system the numeral

The multiplication algorithm, THE MULTIPLICATION ALGORITHM :  Some Class 3...

THE MULTIPLICATION ALGORITHM :  Some Class 3 children in a nearby school had been taught the standard multiplication. Algorithm, and had even done reasonably well in the tests bas

Maximin method -decision making under uncertainty, Decision making under un...

Decision making under uncertainty Various methods are used to make decision in circumstances whereas only the pay offs are identified and the likelihood of every state of natur

Unconditional and conditional probability, Independent and Dependent Events...

Independent and Dependent Events Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event

Ordinary differential equations, Give me the power series solution of Halm'...

Give me the power series solution of Halm''s differential equation

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