Derivation of Finite Difference Approximation
More on Finite Difference Approximation
Derivation of the Heat Equation (Updated Jan 12, 2005)
Equilibrium Temperature Distribution
Basic Concepts: Consistency, Stability, and Convergence
Green's Function and Stability of the Numerical Method
Nouniform Grids. Spectral Method
Numerical Solution for Elliptic PDEs. Laplace Equation
Accuracy and Stability of 5-point FDM for Poisson and Laplace Equations
The 9-point Laplacian and Deferred Correction Technique
Iterative Methods for Sparse Linear Systems
Maximum Principle for Elliptic Problems
Iterative Methods for Linear Systems
Derivation of Winslow's System of Quasi-linear Elliptic PDEs
Finite Difference Method for Time-Dependent PDEs
Theoretical concepts: Consistency, Convergence, and Stability
Kinematic Wave Equation or Linear Scalar Conservation Law
Finite Difference Approximations for the Kinematic Wave Equation
Matrix Stability (New Winter 2009)
More on Matrix Stability Analysis
Proof of Lax-Equivalence Theorem (Updated Feb 25, 2005)
Von Neuman Stability Analysis (Updated Feb 11, 2005)
Finite Differences Methods for Parabolic Equations (Updated Feb 21, 2005)