This collection includes course materials developed by Andrea Prosperetti for MECE 5397: Scientific Computing in Mechanical Engineering. The specific focus are finite-difference methods for elliptic, parabolic and hyperbolic partial differential equations.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. These lecture notes provide an introduction to scientific computing focusing mostly on the numerical solution of partial differential equations of the elliptic, parabolic and hyperbolic types by finite-difference methods. After an introduction to finite-precision numerics and numerical differentiation, the focus is on elliptic equations and the solution of linear algebraic systems. Next, the presentation of methods for parabolic and hyperbolic equations includes the notion of stability and methods for its analysis. Short introductions to methods for ordinary differential equations, weighted-residual methods and verification and validation are also provided.