User:Eml5526.s11.team2/homework4homework4 Xfile/cleveland

=Problem 5.5: =

Guide to Using the ccx Solver
=Problem 5.1=

Concise Formulation of Problem
Specifically we want to determine $$ \displaystyle u^h(x) $$ by solving to following second order differential equation subject to the essential and natural boundary conditions. On the domain defined by,

Find: The Weak Form in Order to Solve for $$ u^h(x) $$ with Following Basis Functions
Solve for $$ \displaystyle u(x) $$ and $$ \displaystyle u^h(x) $$ using the following basis functions until the error $$ \displaystyle e(m) =|u^h(0.5)-u(0.5)| \leq 10^{-6}$$.


 * 1) Polynomial Basis Function  $$ \displaystyle \mathcal{F}_P :=\{ x^j,j=0,1,2,...\} $$
 * 2) Exponential Basis Function $$ \displaystyle \mathcal{F}_e :=\{ e^{jx},j=0,1,2,...\} $$
 * 3) Fourier Basis Function     $$ \qquad \displaystyle \mathcal{F}_F :=\{cos(jx),j=0,1,2,...,sin(kx),k=1,2,...\} $$