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Derive the formula for Newton Raphson Method. Solve the equation \(x^2 + 4x – 9 = 0\) using Newton Raphson method. Assume error precision is 0.01. Discuss drawbacks of the Newton Raphson method.
Not Answered Numerical Method
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Solve the Poison’s equation over the square domain 0 ≤ x ≤ 1.5, 0 ≤ y ≤ 1.5 with f = 0 on the boundary and h = 0.5.
Not Answered Numerical Method
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From the following differential equation estimate y(1) using RK 4th order method.

\(\frac{dy}{dx} + 2x^2y = 4 \enspace with \enspace y(0) = 1\)

[Take h = 0.5]

Not Answered Numerical Method
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Solve the following set of equations using Gauss Seidel method.

x + 2y + 3z = 4

6x – 4y + 5z = 10

5x + 2y + 2z = 25

Not Answered Numerical Method
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Evaluate the following integration using Romberg integration.

\(\int_{0}^{1} \frac{sinx}{x} dx\)

Not Answered Numerical Method
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Calculate the integral value of the function given below from x = 1.8 to x = 3.4 using Simpson’s 1/3 rule.

X 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4
F(x) 0.003 0.778 1.632 2.566 3.579 4.672 7.097 8.429
Not Answered Numerical Method
HamroCSIT User
Find the lowest degree polynomial, which passes through the following points:

X -2 -1 1 2 3 4
F(x) -19 0 2 -3 -4 5

Using this polynomial estimate f(x) at x = 0

Not Answered Numerical Method Asked on 2075 Exam
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What is least squares approximation of fitting a function? How does it differ with polynomial interpolation? Explain with suitable example.
Not Answered Numerical Method
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Calculate a real negative root of following equation using Newton’s method for polynomial.

\(x^4 + 2x^3 + 3x^2 + 4x = 5\)

Not Answered Numerical Method
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What is initial value problem and boundary value problem? Write an algorithm and program to solve the boundary value problem using shooting method.
Not Answered Numerical Method
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