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1- Using fixed point iteration and Newton Raphson methods to solve f(x)=x²-x-2, take n=5 and initial value xo-3.5. Compare between two methods.

1- Using fixed point iteration and Newton Raphson methods to solve f(x)=x²-x-2, take n=5 and initial value xo-3.5. Compare between two methods.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Tutorial Sheet No.4 Numerical Analysis 1- Using fixed point iteration and Newton Raphson methods to solve f(x)=x²-x-2, take n=5 and initial value xo=3.5. Compare between two methods. 2- Repeat above problem for f(x)=cos(x)-2x. Take xo=0.5 and n=5. 3- Using Bisection method to find the root of f(x)=x³-x-3 over the interval [1,2] and n=10. 4- Apply the trapezoidal, Simpson, and n = 6 formulas to compute the integral of sin (x) between 0 and a /2. Calculate the Error bound for two methods. 5- Solve the following systems using Gauss Seidal and Jacobi iteration methods for n=8 and initial values Xº=(0 0 0). i- 3x1 + 2x2 – X3 = 4 ii- 4x1 + 5x2 + x3 = 2 2x1 - X2 + 2x3 = 10 X1 – 2x2 – 3x3 = 7 X1 – 3x2 – 4x3 = 5. Зх1 — Х2 — 2хз— 1. 6- Use Newton-Raphson method to solve the system х3 +у — 1%3D0 уз — х+1%3D0 with the starting value (xo,yo) = (1,0). Take n=4.
Transcribed Image Text:Tutorial Sheet No.4 Numerical Analysis 1- Using fixed point iteration and Newton Raphson methods to solve f(x)=x²-x-2, take n=5 and initial value xo=3.5. Compare between two methods. 2- Repeat above problem for f(x)=cos(x)-2x. Take xo=0.5 and n=5. 3- Using Bisection method to find the root of f(x)=x³-x-3 over the interval [1,2] and n=10. 4- Apply the trapezoidal, Simpson, and n = 6 formulas to compute the integral of sin (x) between 0 and a /2. Calculate the Error bound for two methods. 5- Solve the following systems using Gauss Seidal and Jacobi iteration methods for n=8 and initial values Xº=(0 0 0). i- 3x1 + 2x2 – X3 = 4 ii- 4x1 + 5x2 + x3 = 2 2x1 - X2 + 2x3 = 10 X1 – 2x2 – 3x3 = 7 X1 – 3x2 – 4x3 = 5. Зх1 — Х2 — 2хз— 1. 6- Use Newton-Raphson method to solve the system х3 +у — 1%3D0 уз — х+1%3D0 with the starting value (xo,yo) = (1,0). Take n=4.
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