Numerical Methods for Differential Equations

Numerical Basics

1. Interpolation

• Polynomial Interpolation with Vandermonde Matrix
• Lagrange interpolation
• Newton Basis Polynomial
• Spline Interpolation

2. Approximation and Errors

• Polynomial Interpolation Error
• Approximation through Regression
• Minimum Quadratic Error
• Order of Accuracy

3. Numerical Integration

• Quadrature
• Degree of Correctness for Quadratures

4. Composite Quadrature

• Composite Quadrature
• Romberg’s Extrapolation Method

5. Nonlinear Equations

• Fixed point or Banach’s iteration
• Banach’s fixed point theorem
• Newton-Raphson or Newton’s Method

Numerical Solution of ODEs

• Order of Consistency

Misc

• Numerical Methods Test Prep