Math 411: Numerical Methods

Winter semester 2023

Class Notes

5.2 Basic Numerical Methods for Initial Value Problems

5.3 Higher Order Taylor Methods

5.1 Elementary Theory of Initial Value Problems

5.4 Runge-Kutta Methods (Part 1)

5.4 Runge-Kutta Methods (Part 2)

5.5 Error Control and the Runge-Kutta-Fehlberg Method

5.6 Multistep Methods

5.9 Higher Order Equations and Systems of Ordinary Differential Equations

5.10 Stability (Part 1)

5.10 Stability (Part 2)

10.2 Newton Method for a Single Equation. Order of Convergence

10.2 Newton Method for Nonlinear Systems

10.3 Quasi-Newton Methods

10.4 Steepest Descent Method

9.6 The Singular Value Decomposition (Part 1)

9.6 The Singular Value Decomposition (Part 2)

L.1 Boundary Value Problem for Ordinary Differential Equations. Finite Difference Approximation

L.2 Derivation of Finite Difference Approximation

L.3 Basic Concepts: Consistency, Stability, and Convergence

L.4 Neumann Boundary Conditions.

L.5 Existence and Uniqueness

L.6 General Linear Second Order Equations

L.7 Nonlinear Equations

L.8 Singular Perturbation Problems and Nonuniform Grids

L.9 Spectral Methods

G.1 Finite Element Method (Part 1)

G.1 Finite Element Method (Part 2)

12.0 Derivation of Partial Differential Equations (PDEs)

12.1 Elliptic PDEs (Part 1)

12.1 Elliptic PDEs (Part 2)

12.2 Parabolic PDEs (Part 1)

12.2 Parabolic PDEs (Part 2)