This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: CAAM 336 DIFFERENTIAL EQUATIONS Problem Set 8 Posted Wednesday 27 February 2008. Due Friday 7 March 2008 in class. 1. [50 points] Use the finite element method to solve the differential equation- d dx parenleftBig (1 + x 2 ) du dx parenrightBig = 2 x, &lt; x &lt; 1 subject to the inhomogeneous boundary conditions u (0) = 1 u (1) = / 4 with the approximation space V N given by the piecewise linear hat functions : For N 1, h = 1 / ( N +1), and x k = kh for k = 0 ,...,N + 1, we have 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 . Note that this is similar to Problem 3 of HW 7, but here we have inhomogeneous boundary conditions. You may use the solutions to HW 7 as an aid. (a) Write a MATLAB code that constructs the stiffness matrix and load vector depending on N . (You should be able to compute all necessary integrals by hand and arrive at clean formulas that depend on N or h . Symbolic integration is as inefficient as it is inelegant here.)....
View Full Document
- Fall '09
- Boundary value problem, Boundary conditions, Neumann boundary condition