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ghazala

Member

Registered: 2008-09-05

Posts: 1

Numerical solutions of ODE. Urgent Assignment for friday!!

Hi i dnt knw anythin abt Numerical Soln  of ODe's... ive gt an assignment n it, ive tried a book by kreyzig... bt i still cnt understand a thing... could any1 plz help me??

here are the questions:

1. Consider the IVP given as y' = t - y^2, y(0) = 1

Find y at t = 0.3 using h = 0.1 by using the
(1) Euler Method.
(2) Taylor Series Method of order 2.

2. Consider the IVP y' = t +y, y(0) =2
Find y(0.2) by using the FOrward - Euler Method by using

(1) h = 0.1
(2) h = 0.05

Compare your results with the exact solution and draw your conclusion

3. Consider the IVP y' = -y, y(0) =1
Find y(0.2) by using the Runge - Kutta Method with h = 0.1

4. Consider the IVP

y" - 2y' + y = t

y(0) = 0 , y'(0) = 1

Find y (0.2) by the Forward Euler Method using h = 0.1

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Numerical solutions of ODE. Urgent Assignment for friday!!

Hi ghazala;

I do not know about the Kreyzig book except that it comes highly recommended. I suggest Numerical Analysis by Francis Scheid.

For (1) the Euler method. The Euler method is the simplest numerical technique. It replaces the curve locally with its tangent.
It is intuitively obvious that the tangent is a decent approximation of the curve a small distance away. We say:

(I avoid the use of subscripts because it is easier to program this algorithm on many handhelds without them.)

We run the recursion forward. We get the following table.

So when t = .3, y = .80541, this agrees well with the exact answer of .807621623

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.