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# Numerical Methods

### Examination 2018

#### Group B

2. Why is the study of error important to a computation scientist? Differentiate between inherent and numerical methods

3. Find the root of equation x2 - 4x - 10 = 0 using bisection method where root lies between 3 and 6

4. Find the square root of 3.5 using second order lagrange interpolation polynomial using the following table.

 x 1 2 3 4 5 f(x) 1 1.4142 1.7321 2 2.2361

5. Write a program to calculate the internal using Trapezoidal Rule

6. Solve the following set of equation using Gauss-Jordan Method
3x - 5y + 2z = 15
4x - y + z = 2
x - 3y + 7z = 22

7. Use Classical Runge-Kutta method to estimate y(0.2) when y'(x) = x2 + y2 with y(0) = 0 and h = 0.2

8. Solve the Poisson equation ∇2ƒ = 2x2y2 over the square domain 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 with ƒ = 0 on the boundary and h = 1

### Examination 2019

#### Group B

Attempt any Six question

9 (a) Factorize the matrix
$\begin{bmatrix}1 & 2 & 3\\2 & 8 & 22 \\ 3 & 22 & 82 \end{bmatrix}$ using cholesky's method.

(b) Locate the root equation x2 + x - 2 = 0 using the fixed point method

10 (a) Fit a straight line to the following set of data points.

 x 1 2 3 4 5 6 y 1 3 4 4 5 7

(b) Differentiate between ordinary and partial differential equations with their applications

11. Given the data points.

 1 0 1 2 xi 2 3 4 fi 4 9 16
Estimate the function value f at x = 2.5 using cubic splines.

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