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Solution of Nonlinear Equations
Semester
Subject
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Important Questions
Important Questions
Solution of Nonlinear Equations
Asked in 2081Long Question10 Marks
1.
What are inherent errors? Derive the Newton Raphson method for solving non-linear equation and using this method solve the following equation up to 3 decimal places:
[10]
Asked in 2080Short Question5 Marks
2.
Define the terms approximate error and relative approximate error? Discuss the working of Half Interval method for finding the roots of non-linear equation. [5]
Asked in 2080Long Question10 Marks
3.
How secant methods differs from Newton Raphson method? Derive the formula for Secant Method. Solve the equation using Secant method. Assume error precision as 0.01. Discuss the drawbacks of the Newton Raphson method.
[10]
Asked in 2079Short Question5 Marks
4.
What is fixed point iteration method? How can it converge to the root of a non-linear equation? Also explain the diverging cases with suitable examples. [5]
Asked in 2079Short Question5 Marks
5.
Calculate a real root of the following function using bisection method correct upto 3 significant figures.
[5]
Asked in 2079Long Question10 Marks
6.
How secant method can approximate the root of a non-linear equation? Explain with necessary derivation. Estimate a real root of following equation using secant method. Assume error precision of 0.01.
[10]
Asked in 2078Short Question5 Marks
7.
Calculate the real root of the given equation using fixed point iteration correct up to 3 significant figures.
[5]
Asked in 2078Short Question5 Marks
8.
How the half-interval method can be estimate a root of a non-linear equation? Find a real root of the following equation using the half-interval method to correct up to two decimal places.
[5]
Asked in 2078Long Question10 Marks
9.
How can Horner’s rule be used to evaluate the f(x) and f(x) of a polynomial at a given point? Explain. Write an algorithm and program to calculate a real root of a polynomial using Horner’s rule. [10]
Asked in 2077Short Question5 Marks
10.
Define the terms true error and relative error? Use Horner' method to evaluate polynomial at x = 3 and write down its algorithm.
[5]
Asked in 2077Long Question10 Marks
11.
Derive the formula for Newton Raphson Method. Solve the equation using Newton Raphson method. Assume error precision is 0.01. Discuss drawbacks of the Newton Raphson method.
[10]
Asked in 2075Short Question5 Marks
12.
Calculate a real negative root of following equation using Newton’s method for polynomial.
[5]
Asked in 2075Long Question10 Marks
13.
What is non-linear equation? Derive the required expression to calculate the root of non-linear equation using secant method. Using this expression find a root of following equation.
[10]