Explain the importance of error analysis in numerical methods with suitable example. Out of Bisection method...

Explain the importance of error analysis in numerical methods with suitable example.
Out of Bisection method and secant method which one is better and why? Solve one application based problem using that method.
Use Newton-Raphson Method to find the root of trigonometric function correct up to seven decimal places. (Trigonometric function should be complex)
Solve one problem which is based on the application of Interpolation.
Using numerical differentiation solve one application based problem. (Use central difference approximation and problem must include first order as well as second order derivatives)
Out of Trapezoidal rule and Simpson’s 1/3^rd rule which one is better explain in detail. Also solve one application based problem using that rule. Compare the exact and approximate result to compute the relative error.

(I saw the same question already uploaded in the chegg but i need other numbers )

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Colby Messinger answered 1 year ago

Explain the importance of error analysis in numerical methods with suitable example. Out of...

Explain the importance of error analysis in numerical methods with suitable example. Out of Bisection method and secant method which one is better and why? Solve one application based problem using that method. Use Newton-Raphson Method to find the root of trigonometric function correct up to seven decimal places. (Trigonometric function should be complex) Solve one problem which is based on the application of Interpolation. Using numerical differentiation solve one application based problem. (Use central...

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Write Matlab programs implementing the algorithms based on bisection,Newton, and secant method for numerical solution of...

Write Matlab programs implementing the algorithms based on bisection,Newton, and secant method for numerical solution of scalar nonlinear equa-tions. Use these programs to compute approximations to real roots of the following equations: exp(x)−3x^2=0, (1) x^3=x^2+x+1, (2) exp(x) =1/(0.1 +x^2), (3) and x= 1 + 0.3 cos(x). (4) Use an error tolerance tol=10^(−12). Display the obtained approximations to the roots of these equations, and compare the number of iterations, starting with the same initial values x0 for bisection and Newton methods,...

MATH505 – NUMERICAL METHODS AND ANALYSIS 6. Out of Trapezoidal rule and Simpson’s 1/3rd rule which...

MATH505 – NUMERICAL METHODS AND ANALYSIS 6. Out of Trapezoidal rule and Simpson’s 1/3rd rule which one is better explain in detail. Also solve one application based problem using that rule. Compare the exact and approximate result to compute the relative error.

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Explain the importance of error analysis in numerical methods with suitable example. Out of Bisection method...

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