Exercises

  1. In what parts of the (x,y)-plane is the following equation elliptic?

    \begin{displaymath}u_{xx}+4u_{xy}+(x^2+4y^2)u_{yy}=Sin(xy)\end{displaymath}

  2. The .... conduction equation $u_t=u_{xx}$ is approximated by

    \begin{displaymath}\frac{U_{i,j+1}-U_{i,j-1}}{2k}=\frac{U_{i-1,j}-2U_{i,j}+U_{i+1,j}}{h^2}\end{displaymath}

    a) Determine the truncation error.
    b) Investigate the stability using Von-Nenmann method.