Numerical Differential Equations

4 credits

Finite difference approximation. Initial value ODEs: explicit, implicit, accuracy, stability, convergence, Runge-Kutta and multipoint methods, stiff systems. Boundary value ODEs: shooting and equilibrium method. PDEs: stability and accuracy. Hyperbolic PDEs: central and upwinding methods, linear advection, Burgers equation. Parabolic PDEs: convection-diffusion equation, multidimensional problems. Elliptic PDEs: direct solution, iterative solution, multigrid method. Fourier spectral method. Prerequisites: graduate standing or consent of instructor.