April

 Monday Tuesday Wednesday Thursday Friday
  2 3 Classes start:

Handouts - 1 , 2 , 3 , 4 & 5

Lagrange Polynomial

4 5
8 Assignment No.1 due

Cubic Spline, Finite Difference.

9 10

Finite Difference formulae, Pade Approximations

11 12
15

Assignment No.2 due

Modified Wave Number, Finite difference form for non-uniform mesh spacing

Trapezoidal, rectangular and Simpson rule, error analysis

16 17

Trapzoidal rule with end correction, Richardson extrapolation, Romberg integration

18 19
22 Assignment No.3 due

Adaptive quadrature, Gauss quadrature

23 24

Gauss Quadrature, remedies for singularities in integrand

Numerical solution of ODE's, Euler's method, different classes of solution methods

25 26
29Assignment No.4 due

Stability Analysis of Numerical Schemes,
Implicit Euler
30      


 

May

 Monday Tuesday Wednesday Thursday Friday

 
 
  1

Amplitude and Phase Error, Trapezoidal method, predictor and corrector methods, 2nd order Runge Kutta methods
2 3
 
 
6 Assignment No.5
due

General form of Runge Kutta Methods, 2nd order R-K method, stability and accuracy, phase error,  Multi-step methods

7 8

Mid Term Exam

Syllabus : Everything covered till (and including)1st May


 

9 10


 

13
 Assignment No.6
due

Multi-step methods, Leapfrog method, Adam Bashforth Method, System of First Order Ordinary Differential Equations
 

14
 
 
15

System of First Order ODE's, Boundary Value Problems, Shooting Methods

16
 
 
 
 
 
17
20
  Assignment No.7 due

Shooting Methods and Direct Methods for ODE's

PDE's

21 22

PDE's semi-discretisation, stability analysis, Von Neumann stability analysis, Modified wave number analysis

23
 
 
 
 
24
 
Modified Wave Number Analysis, Implicit Time Advancement, Accuracy via modified equation, Du-Fort Frankel Method
 
27 28 29

Assignment No.8 due

Multi dimensions, Implicit methods in higherdimensions, Approximate factorisation

30
 
 
 
 
 
31


 
 

June

 Monday Tuesday Wednesday Thursday Friday
3Assignment No.9 due

Alternating Direction Implicit Methods, Elliptic partial differential equations, Iterative Solution Methods, Point Jacobi Method, Gauss Seidel Method

4 5

Point Jacobi Method,

Gauss Seidel Method,

Successive Over Relaxation (SOR)

6 7
10 11 12

End Term Exam

13 14