$Numerical$ $Analysis$

• Finding roots

• Polynomial and transcendental equations

• Bisection method  

• Regula-Falsi method  

• Secant method  

• Newton – Raphson method  

• Muller’s method (for 2nd degree) 

• Chebyshev method (for 2nd degree) 

• Graffe’s root square method  

Interpolation 

• Difference operators  

• Forward difference  

• Backward difference 

• Central difference  

• Shifting or translation  

• Average operator  

• Differential operator  

• Formulas  

• Newton’s backward and forward interpolation  

• Gaussian central difference interpolation  

• Stirling interpolation  

• Bessel interpolation

• Lagrange formula with unequal intervals (linear, quadratic, cubic)  

• Divided difference  

• Newton’s divided difference  

• Errors

Linear equations 

• Direct method  

• Gauss – elimination  

• Gauss- Jordon 

• L-U Decomposition 

• Choleski’s Decomposition  

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• Iterative Method 

• Jacobi-iteration method 

• Gauss- Siedal iteration 

• Relaxation method 

Differentiation and extreme value 

• Methods based on interpolation formulae  

• Newton’s forward and backward  

• Stirlling’s formula 

• Maxima and minima

• Methods based on divided difference 

• Lagrange’s divided difference interpolation 

 

ODEs 

• Single step 

• Taylor method 

• Picard method 

• Euler’s method 

• Euler’s modified  

• Runge-Kutta 

• Multi step 

• Milne-Simpson method 

Integration 

• Quadrature form 

• Newton cote formula 

• Trapezoidal rule  

• Simpson 1/3 rule  

• Simpson 3/8 rule  

• Boole’s rule   

• Waddle’s rule 

 

• Methods based on numerical integration  

• Euler-Maclaurin formula  

• Gauss–Chebyshev integration formula 

• Triple point formula