hw12Apr2008

hw12Apr2008 - CAAM 336 DIFFERENTIAL EQUATIONS Problem Set...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CAAM 336 DIFFERENTIAL EQUATIONS Problem Set 12 Due Wednesday 9 April 2008 in class. 1. [60 points] We wish to approximate the solution to the heat equation u t- 2 u x 2 = 100 tx, x 1 , t with homogeneous Dirichlet boundary conditions u (0 , t ) = u (1 , t ) = 0 and initial condition u ( x, 0) = 0 using the finite element method (method of lines). Let N 1, h = 1 / ( N + 1), and x k = kh for k = 0 , . . . , N + 1. We shall construct approximations using the hat functions k ( x ) = ( x- x k- 1 ) /h, x [ x k- 1 , x k ); ( x k +1- x ) /h, x [ x k , x k +1 ); , otherwise . The approximate solution shall have the form u N ( x, t ) = N summationdisplay k =1 a k ( t ) k ( x ) . (a) Write down the system of ordinary differential equations that determines the coefficients a k ( t ), k = 1 , . . . , N . Specify the entries in the mass and stiffness matrices and the load vector....
View Full Document

This note was uploaded on 01/21/2012 for the course CAAM 330 taught by Professor Tompson during the Fall '09 term at UVA.

Page1 / 2

hw12Apr2008 - CAAM 336 DIFFERENTIAL EQUATIONS Problem Set...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online