Numerical methods

Hi guys here is a list of all numerical methods that will be used for computations by almost all kinds of engineers……..

 

Calculus and Fundamentals

  1. Calculus
  2. Mean Value Theorem
  3. Fundamental Theorem of Calculus
  4. Fundamental Theorem of Algebra
  5. Big “O” Truncation Error
  6. Complex Numbers
  7. Roots of Cubic Equations
  8. Roots of Quartic Equations
  9. Using MATLAB for Numerical Analysis

The Solution of Nonlinear Equations f(x) = 0

  1. Fixed Point Iteration
  2. Bisection Method
  3. False Position or Regula Falsi Method
  4. Newton-Raphson Method
  5. Secant Method
  6. Muller’s Method
  7. Aitken’s Method & Steffensen’s Acceleration
  8. Halley’s Method
  9. Nonlinear Systems
  10. Horner’s Method
  11. Lin-Bairstow Method
  12. Brent’s Method
  13. Broyden’s Method
  14. Graeffe’s Method
  15. Jenkins-Traub Method
  16. Laguerre’s Method

The Solution of Linear Systems AX = B

  1. Triangular Systems and Back Substitution
  2. Gauss-Jordan Elimination and Pivoting
  3. Tri-Diagonal Matrices
  4. Inverse Matrix
  5. Hilbert Matrix
  6. LU Factorization
  7. Cholesky, Doolittle and Crout Factorizations
  8. Jacobi and Gauss-Seidel Iteration
  9. Ill-Conditioned Linear Systems
  10. Successive Over Relaxation – SOR
  11. Pivoting Methods
  12. Iterative Refinement
  13. Row Reduced Echelon Form
  14. Homogeneous Linear Systems
  15. Kirchoff’s Law
  16. Leontief Model
  17. Linear Programming

Interpolation and Polynomial Approximation

  1. Maclaurin and Taylor Series
  2. Lagrange Polynomial Interpolation and Approximation
  3. Newton Interpolation Polynomial
  4. Hermite Polynomial Interpolation
  5. Cubic Splines
  6. B-Splinesplines
  7. Bézier Curves Bézier Curves
  8. Chebyshev ApproximationPolynomial
  9. Pade Approxim
  10. ation
  11. Rational Approximation
  12. Aitken’s and Neville’s Interpolation
  13. Orthogonal Polynomials
  14. Legendre Polynomials
  15. Computation of Pi
  16. Catenary

Curve Fitting

  1. Least Squares Lines
  2. Least Squares Polynomials
  3. Nonlinear Curve Fitting
  4. Logistic Curve
  5. FFT and Trigonometric Polynomials
  6. Signal Processing
  7. Conic Fit
  8. Curvature

Numerical Differentiation

  1. Numerical Differentiation
  2. Richardson Extrapolation
  3. Automatic Differentiation

Numerical Integration

  1. Riemann Sums
  2. Midpoint Rule
  3. Newton-Cotes Integration
  4. Trapezoidal Rule for Numerical Integration
  5. Simpson’s Rule for Numerical Integration
  6. Romberg Integration
  7. Adaptive Simpson’s Rule
  8. Gauss-Legendre Quadrature
  9. Gauss-Kronrod Quadrature
  10. Monte Carlo Pi
  11. Monte Carlo Integration
  12. Chebyshev Quadrature
  13. Gauss-Laguerre Quadrature

Solution of Differential Equations

  1. Euler’s Method for O. D. E.’s
  2. Taylor Series Method for D.E.’s
  3. Runge-Kutta Method
  4. Runge-Kutta-Fehlber Method
  5. Adams-Bashforth-Moulton Method
  6. Milne-Simpson’s Method
  7. Predictor-Corrector Methods for O.D.E.’s
  8. Shooting Methods for O.D.E.’s
  9. Finite Difference Method for O.D.E.’s
  10. Galerkin’s Method
  11. Lotka-Volterra Model
  12. Pendulum
  13. Projectile Motion
  14. Lorenz Attractor
  15. Duffing Equation
  16. van der Pol System
  17. Harvesting Model
  18. Spring Mass Oscillations
  19. Stiff Differential Equations
  20. Painlevé Property
  21. Picard Iteration
  22. Difference Equations
  23. Cobweb Models

Solution of Partial Differential Equations

  1. Finite Difference Method
  2. Crank-Nicolson Method
  3. Elliptic PDE’s
  4. Vibrating Drum
  5. Vibrating String
  6. Dirichlet Problem
  7. Harmonic Functions

Eigenvalues and Eigenvectors

  1. Eigenvalues and Eigenvectors
  2. Power method
  3. Jacobi method
  4. HouseholderTransformations
  5. QR method
  6. Compartment Model
  7. Earthquake Model
  8. Matrix Exponential
  9. Faddeev-Leverrier Method
  10. Hessenberg Factorization
  11. Wielandt Deflation
  12. Eigenfaces
  13. Principal Axis
  14. The Jordan Form

Numerical Optimization

  1. Golden Ratio Search
  2. Fibonacci Search
  3. Quadratic Search
  4. Nelder Mead Method
  5. Steepest Descent Gradient Search
  6. Powell’s Method
  7. Newton’s Search for a Minimum

Ordinary Differential Equations

  1. Series Solutions Frobenius Method
  2. Airy Functions
  3. Bessel Functions
  4. Exact Differenti Equations
  5. Homogeneous Linear Differential Equations
  6. Separable Differential Equations
  7. Variation of Parameters
  8. Autonomous Systems
  9. Belousov-Zhabotinskii Model
  10. Hodgkin-Huxley Model
  11. Michaelis-Menten Model
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1 Comment »

  1. 1
    Quant Says:

    thanks, Finite element method is also widely used for the Solution of Partial Differential Equations.


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