SS Numerical Methods

Numerical Basics

Interpolation

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

Interpolation, Approximation and Errors

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

Numerical Integration

• Quadrature
  • Left-rectangle rule
  • Right rectangle rule
  • Mid-point rule
  • Trapezoid rule
  • Simpson’s Rule
• Degree of Correctness for Quadratures

Composite Quadrature

• Composite Quadrature
• Romberg’s Extrapolation Method

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