x # Computational Techniques

IIT Madras, , Prof. Niket Kaisare

Updated On 02 Feb, 19

## Lecture 26: Mod-07 Lec-26 Ordinary Differential Equations (initial value problems) Part 2

4.1 ( 11 )

###### Lecture Details

Computational Techniques by Dr. Niket Kaisare, Department of Chemical Engineering, IIT Madras. For more details on NPTEL visit httpnptel.iitm.ac.in

### COURSE LAYOUT

Week-1: Introduction & Approximations
Motivation and Applications
Accuracy and precision; Truncation and round-off errors; Binary Number System; Error propagation
Week-2: Linear Systems and Equations
Matrix representation; Cramers rule; Gauss Elimination; Matrix Inversion; LU Decomposition;
Week-3: Linear Systems and Equations
Iterative Methods; Relaxation Methods; Eigen Values
Week-4: Algebraic Equations: Bracketing Methods
Introduction to Algebraic Equations
Bracketing methods: Bisection, Reguli-Falsi;
Week-5: Algebraic Equations: Open Methods
Secant; Fixed point iteration; Newton-Raphson; Multivariate Newtons method
Week-6: Numerical Differentiation
Numerical differentiation; error analysis; higher order formulae
Week-7: Integration and Integral Equations
Week-8: Regression
Linear regression; Least squares; Total Least Squares;
Week-9: Interpolation and Curve Fitting
Interpolation; Newtons Difference Formulae; Cubic Splines
Week-10: ODEs: Initial Value Problems
Introduction to ODE-IVP
Eulers methods; Runge-Kutta methods; Predictor-corrector methods;
Week-11: ODE-IVP (Part-2)
Extension to multi-variable systems; Adaptive step size; Stiff ODEs
Week-12: ODEs: Boundary Value Problems
Shooting method; Finite differences; Over/Under Relaxation (SOR)

#### 0

0 Ratings
55%
30%
10%
3%
2% Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college. 