IOE Syllabus – Numerical Methods for BME

NUMERICAL METHODS

5.2.

Maxima and minima

SH603

5.3.

Newton-Cote general quadrature formula

Lecture

:

3

Year

: III

5.4.

Trapezoidal, Simpson’s 1/3, 3/8 rule

5.5.

Romberg integration

Tutorial

:

1

Part

: I

5.6.

Gaussian integration ( Gaussian – Legendre Formula 2 point and 3 point)

Practical

:

3

6.

Solution of ordinary differential equations

(6 hours)

Course objective:

6.1. Euler’s and modified Euler’s method

To introduce numerical methods used for the solution of engineering problems. The

6.2.

Runge Kutta methods for 1st and 2nd order ordinary differential equations

course emphasizes algorithm development and programming and application to

6.3.

Solution of boundary value problem by finite difference method and shooting

realistic engineering problems.

method.

1. Introduction, Approximation and errors of computation

(4hours)

7. Numerical solution of Partial differential Equation

(8 hours)

1.1.

Introduction, Importance of Numerical Methods

7.1.

Classification of partial differential equation(Elliptic, parabolic, and Hyperbolic)

1.2. Approximation and Errors in computation

7.2.

Solution of Laplace equation ( standard five point formula with iterative method)

1.3.

Taylor’s series

7.3. Solution of Poisson equation (finite difference approximation)

1.4. Newton’s Finite differences (forward , Backward,

central difference, divided

7.4.

Solution of Elliptic equation by Relaxation Method

difference)

7.5. Solution of one dimensional Heat equation by Schmidt method

2. Solutions of Nonlinear Equations

(5 hours)

Practical:

Algorithm and program development in C programming language of following:

2.1.

Bisection Method

1.

Generate difference table.

2.2.

Newton Raphson method ( two equation solution)

2.

At least two from Bisection method, Newton Raphson method, Secant method

2.3.

Regula-Falsi Method , Secant method

3.

At least one from Gauss elimination method or Gauss Jordan method. Finding largest

2.4.

Fixed point iteration method

Eigen value and corresponding vector by Power method.

2.5. Rate of convergence and comparisons of these Methods

4.

Lagrange interpolation. Curve fitting by Least square method.

5.

Differentiation by Newton’s finite difference method. Integration using Simpson’s 3/8

3. Solution of system of linear algebraic equations

(8 hours)

rule

3.1.

Gauss elimination method with pivoting strategies

6.

Solution of 1st order differential equation using RK-4 method

3.2.

Gauss-Jordan method

7.

Partial differential equation (Laplace equation)

3.3.

LU Factorization

8.

Numerical solutions using Matlab.

References:

4.

Interpolation

(8 hours)

1.

Dr. B.S.Grewal, “Numerical Methods in Engineering

and

Science “, Khanna

4.1.

Newton’s Interpolation ( forward, backward)

Publication.

4.2.

Central difference interpolation: Stirling’s Formula, Bessel’s Formula

2.

Robert J schilling, Sandra l harries , ” Applied Numerical Methods for Engineers using

4.3.

Lagrange interpolation

MATLAB and C.”, Thomson Brooks/cole.

4.4.

Least square method of fitting linear and nonlinear curve for discrete data and

3.

Richard L. Burden, J.Douglas Faires, “Numerical Analysis”,

Thomson / Brooks/cole

continuous function

4.

John. H. Mathews, Kurtis Fink ,”Numerical Methods Using MATLAB” ,Prentice Hall

4.5.

Spline Interpolation (Cubic Spline)

5.

publication

with MATLAB” ,

JAAN KIUSALAAS , “Numerical Methods in Engineering

5.

Numerical Differentiation and Integration

(6 hours)

Cambridge Publication

Unit

Chapter

Topics

Marks

1

1 & 2

all

16

2

3

all

16

3

4

all

16

4

5

all

16

6

6.1, 6.2

5

6

6.3

16

7

all

Total

80