Results 1 to 2 of 2

Math Help - Unconditionally stable scheme for solving first order system of PDEs

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    9

    Unconditionally stable scheme for solving first order system of PDEs

    Hello,

    I would like to numerically solve the following system of PDEs using a stable computational scheme. The system involves three equations and three unknowns ( q_x, q_y, and p). I've tried to solve this system using an explicit scheme, but I found that the solution could become unstable. An implicit scheme may work, but then how would I deal with the three unknowns in a computationally efficient fashion?

    Could someone suggest a stable scheme to numerically solve this system?

    <br />
\[<br />
A\frac{{\partial p}}{{\partial t}} + Bp = \frac{{\partial q_x }}{{\partial x}} + \frac{{\partial q_y }}{{\partial y}}<br />
\]<br />

    <br />
\[<br />
\frac{{\partial q_x }}{{\partial t}} = \frac{{\partial p}}{{\partial x}}<br />
\]<br />

    <br />
\[<br />
\frac{{\partial q_y }}{{\partial t}} = \frac{{\partial p}}{{\partial y}}<br />
\]<br />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jul 2010
    Posts
    9
    Perhaps one way of proceeding is to set this up as a block tridiagonal system of equations, and then solve for all of the unknowns using an efficient algorithm.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. System of PDEs question
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 12th 2011, 12:38 PM
  2. Solving a System of First Order Differential Equations
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 16th 2010, 11:08 PM
  3. Relaxation Scheme for system Au=f
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: September 20th 2010, 05:51 PM
  4. Classification of Linear 2nd-Order PDEs
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: August 29th 2010, 06:44 AM
  5. Derive a third order accurate scheme
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 24th 2008, 03:41 AM

Search Tags


/mathhelpforum @mathhelpforum