NUMERICAL METHODS

NUMERICAL METHODS

Errors in Numerical Computation.: Their types, analysis and estimation, numerical instabilities in computation.

Solutions to Transcendental and Polynomial equations: Bisection method, secant method, Regula Falsi method, Newton Raphson method for polynomial equations.

Solutions to System of Linear Algebraic Equations.: Cramers rule, Gauss elimination method, Gauss Jordan method, Triangularization methods- Gauss Siedel method of iteration.

Interpolation and Approximation.: Linear interpolation and high order interpolation using Lagrange and Newton Interpolation methods, finite difference operators and interpolation polynomials using finite differences. Approximations- least square approximation technique, linear regression.

Numerical Differentiation.: Methods based on interpolation and finite differences.

Numerical Integration.: Trapezoidal rule, mid-point method, Simpsons 1/3rd and 3/8th rule.

Solutions to ordinary differential equations .: Taylor series method, Picards method of successive approximation. Eulers method, Eulers predictor and corrector method. Runge Kutta method for 2nd and 4th order. Initial and boundary value problems.

Numerical Optimisation.: Golden section search, Brents method, minimisation using derivatives, introduction to linear programming

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