Computer Oriented Numerical Methods — Summer 2018

Find the root of the equation x3 – x- 4= 0 using the Bisection method. Perform iterations until the accuracy till four significant digit.

Find the root of the equation x4 +24x -50 =0 correct up to three significant digits using Birge-Vieta method. Assume the initial value of the root = 1.5

(i) Explain total numerical error. How can one control numerical errors ? (ii) State Descartes rule of sign. Use it to determine the number of positive and negative roots of the polynomial equation : x4 – 3x3 + 2x2 + 20x – 20 =0

Use secant method to find a root of the following equation x3 – 5x+3 = 0, correct up to three decimal places.

Use Newton-Raphson method to find a root of the following equation x3 – 4x-9 = 0, correct up to three decimal places between 2.625 and 3.

From the following table, find y when x = 0.4 using Lagrange’s interpolation formula. X 0.3 0.5 0.6 y 0.61 0.69 0.72

Fit a straight line of the form y = a + bx, to the following data : x 0.1 0.2 0.3 0.4 0.5 0.6 y 5.1 5.3 5.6 5.7 5.9 6.1

Compute value of y at x=0.02 using suitable interpolating polynomial X 0.0 0.1 0.2 0.3 0.4 Y 1.0000 1.1052 1.2214 1.3499 1.4918

Fit an exponential curve for the following data: x 600 500 400 350 y 2 10 26 61

Compute the second order derivative for the following set of data values at x=3 X 0 1 2 F(x) -5 1 9 25

2 1 ( x) Evaluate e 2 dx using trapezoidal rule for four intervals.1

The distance (s) covered by a car in a given time (t) is given in the following table : Time (minutes) 10 12 16 17 22 Distance (kms) 12 15 20 22 32 Find speed of the car at t=14 minutes.1

Evaluate2 42 ( x 2  2 x ) d x07 using Gauss Quadrature formula.

Solve the following system of simultaneous linear equations using Gauss- Elimination method: 2x+8y+2z=14 x+6y-z=13 2x-y+2z=5

Given d y / d x  1  y 2 with y(0)=0,y(0.2)=0.2027,y(0.4)=0.4228,y(0.6)=0.6841. compute y(0.8) using Milne simpson’s Predictor-Corrector method.

Solve the following system of simultaneous linear equations using Gauss- Seidel method: 10x+y+2z = 44 2x+10y+z = 51 x+2y+10z = 61

Given d y / d x  1  y 2 with y(0)=0,y(0.2)=0.2027,y(0.4)=0.4228,y(0.6)=0.6841. compute y(0.8) using Adam-Bashforth Predictor-Corrector method.