Re: PDE (Finite_difference & Finite_element) doubt ?

On Jan 17, 1:02 pm, Nimo <azeez...@xxxxxxxxx> wrote:
On Jan 17, 4:12 am, Matt <matt271829-n...@xxxxxxxxxxx> wrote:



On Jan 16, 9:45 pm, Nimo <azeez...@xxxxxxxxx> wrote:

On Jan 16, 7:16 pm, Nimo <azeez...@xxxxxxxxx> wrote:

On Jan 16, 11:10 am, Nimo <azeez...@xxxxxxxxx> wrote:

Nimo wrote:
Un-like every time I keep
asking something,
and people are confusing etc,etc,
to avoid all that,
I'm writing everything in brief.

Thanks.
Let's go to the problem
-------------

Well,
first things first
just glimpses of everything
I studied up to now.

1) Partial_Differential_Equations
(I'm concerned with first and second order only)

2)  Can be classified depending up on their
     Boundary conditions.

Hyperbolic____Wave-equation__ Cauchy(boundary)
Elliptic____Laplace-equation____Dirichlet or Neumann.
Parabolic____Heat-equation____Dirichlet or Neumann.

3) Analytical Solution:-

       a)  one of the easiest way is
            'Separation of variables to
            obtain a system of de-coupled ODEs'

       b)   variable-transformation,
             concept of 'convection-diffusion'
            (CD equation) form.

4) Numerical Solution:-

    a) Finite-difference,
    b) Finite-element.

Yes, now my doubt is
for a given PDE, we can
find a solution
analytically,

but in my calculus book
Using a CD equation
author has used
Forward and centered differences
and has written finite
difference equations
in matrix forms as
( A u = B ),

and again
coming to the concept of
(4b), there too I'm confused

 [     Lu(.) = f
       u(.) =(x,y,z,t)
       L = differential operator
       f = independent function    ]

all these stuff is there
and more over
there is no example problem there
to analyze the concepts.

So,
how exactly I can use the above 2
techniques,
1) Can you please tell me more
generally ?
2) What are their practical uses ?

None for help..!

no need of any descriptions

please tell me when and where can I implement this
techniques ?

I mean for  an ODE
I know its uses and I can solve it by any one of the
techniques

(1) Taylor's series method,
(2) Euler's method,
(3) Modified Euler's Method,
(4) Picard's method,
(5) Runge - kutta method,
(6) Predictor - corrector methods,
   (a)  Milne Predictor corrector formula,
   (b)  Adams Modulation method.

but,

how to analyze the above techniques

USES.
and when can I implement them.

---
none for the help.
is this really so much, confusing

It may be not so much confusing as too wide-ranging for someone to
answer in a forum like this. People write whole thick books about the
sort of questions you're asking.

yeah I can understood the situation,
what people are thinking,
Just provide me few examples you know,so that
at-least I'll try to understand my-self.

My basic & original questions are,

1) When and where this techniques can be implemented ?
2) What is the fundamental difference between those 2 methods ?

Thanks :)
Can you refer any problem you have dealt regarding this
topics, so that I can learn it.

any help please ?
.

Relevant Pages