ENGR391_Final_2007

# ENGR391_Final_2007 - ENGR 391 FINAL EXAM FACULTY OF...

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ENGR 391 FINAL EXAM ENGR-391 NUMERICAL METHODS FOR ENGINEERS Student’s Name: I.D.: Duration 3 hours PROBLEM 1 [Solving Nonlinear Equations] [20 marks] 1. Practice Solve the following nonlinear equation using the secant method with x 0 =0 and x 1 =1: 1 ) ( 3 - + = x x x f Use 5 iterations. Check your result. 2. Theory - What is the main difference between Newton-Raphson method and secant method? - Sketch the bisection and the Newton-Raphson method. PROBLEM 2 [Solving Systems of Linear Equations] [40 marks] 1. Practice Solve the following system of linear equations: = + + - - = + - = + - 15 5 2 21 8 4 7 4 z y x z y x z y x 1 FACULTY OF ENGINEERING AND COMPUTER SCIENCE DEPARTMENT OF MECHANICAL ENGINEERING

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ENGR 391 FINAL EXAM a- Using LU decomposition b- Using Gauss-Seidel method (3 iterations), choose as initial guesses: y=z=0 c- Check your results d- Compare the two methods 2. Theory - Ill conditioning of equations occurs when the determinant of [A] is close to zero? True / I really do not know / False
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## This note was uploaded on 01/11/2011 for the course ENGR 391 taught by Professor Hoidick during the Spring '09 term at Concordia Canada.

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ENGR391_Final_2007 - ENGR 391 FINAL EXAM FACULTY OF...

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