MTH603 Final Term Mega File

MTH603 finalterm huge file

Numerical analysis (Virtual University of Pakistan)

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MTH603 finalterm huge file

Numerical analysis (Virtual University of Pakistan)

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File Version v11.02.02 Prepared For: Final Term

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File Version updated on 7/24/2011

Virtual University

of Pakistan

----:Table of Content:----

Table of Content

TABLE OF CONTENT ..................................................................................................................................................................... 1

ERROR .......................................................................................................................................................................................... 6

Method of Iterations ................................................................................................................................................................. 13

Graeffe’s Root Square Method .................................................................................................................................................. 20 LINEAR EQUATIONS ............................................................................................................................................................................. 20 Gaussian Elimination Method ................................................................................................................................................... 20 Guass-Jordan Elimination Method ............................................................................................................................................ 23 Jacobi’s Iterative Method .......................................................................................................................................................... 23 Gauss-Seidel Iteration Method .................................................................................................................................................. 25

Matrix Inversion ........................................................................................................................................................................ 28 EIGEN VALUE PROBLEMS ...................................................................................................................................................................... 28 Power Method ........................................................................................................................................................................... 28 Jacobi’s Method ......................................................................................................................................................................... 31 INTERPOLATION .................................................................................................................................................................................. 35 Forward Differences .................................................................................................................................................................. 37 Backward Differences ................................................................................................................................................................ 38 Divided Differences .................................................................................................................................................................... 40 By Newton’s Forward Difference Formula ................................................................................................................................. 47 b) By Lagrange’s Formula ......................................................................................................................................................... 48 Langrange’s Interpolation ......................................................................................................................................................... 49 Differentiation Using Difference Operators ............................................................................................................................... 50 NUMERICAL INTEGRATION .................................................................................................................................................................... 51 Trapezoidal Rule ........................................................................................................................................................................ 51 Simpson’s 1/3 and 3/8 rules ...................................................................................................................................................... 55

Taylor Series Method ................................................................................................................................................................. 57 Euler Method ............................................................................................................................................................................. 59 Euler Modified Method:............................................................................................................................................................. 60 Runge-Kutta Method ................................................................................................................................................................. 61