iMechanica - Solution of system of Differential equations - Comments

Morse and Feshbach might help

Mogadalai Gururajan — Sun, 21 Jan 2007 12:48:00 -0500

Dear Sandip,

Even for a general solution, you would need to know the boundary conditions; that is because, when you write the solution, to calculate the constants, you have to use the bc's; depending on the bc's, for the same equation, the solutions could be different. Even if you are looking for a numerical solution, you need to use the bc's to modify the A(t) matrix. As this wiki page notes,

general solutions of ordinary differential equations involve arbitrary constants, but solutions of partial differential equations involve arbitrary functions. A solution of a partial differential equation is generally not unique; additional conditions must generally be specified on the boundary of the region where the solution is defined.

These type of equations are dealt in detail by Morse and Feshbach in their Methods of theoretical physics. That might also help. Best of luck!

Dear Wei and Mogadalai

Sandip Haldar — Sat, 20 Jan 2007 04:19:17 -0500

Dear Wei and Mogadalai,

Thanks for your reply.

I have attached a pdf file containing the detail of the problem.

Sandip Haldar

Some more information would help

Mogadalai Gururajan — Thu, 18 Jan 2007 11:58:14 -0500

Dear Sandip,

As Wei Hong noted, could you tell a bit more about the problem (or, how you arrived at this equation)?

What are the boundary conditions?

Since you are in IISc, you might also want to talk to Prof. Anindya Chatterjee of Mechanical Engineering department -- he might be able to help you out too.

Could you tell us more about the problem?

Wei Hong — Thu, 18 Jan 2007 11:01:25 -0500

The system has time-dependent eigenvalues/eigenvectors, which are not easy (or impossible if n is large and A has a general form) to calculate.

Do you mind sharing a little bit more about your actualy problem, and why you decide to use eigenvalue approach?

My feeling is that if the problem does not contain any eigenvalue information physically, it won't benifit from an eigenvalue approach.

Solution of system of Differential equations

Sandip Haldar — Thu, 18 Jan 2007 04:31:01 -0500

Dear Wei and Mogadalai,

As mentioned earlier I am trying to solve for a vector {x} from

{x'}=[A(t)]{x}

where [A(t)] is known matrix of size (2X2) at the max 4x4, elements and are functions of "t".

{x} is a vector (nX1) function of 't'

{x'} is derivative of {x} with respect to 't'.

I want to solve this system by Eigenvalue ,Eigenvector approach.

In this edit, I have attached a PDF file that details the problem on hand.

Looking forward to your help

Thanks

Sandip