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Numerical Methods Practical Questions.txt
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Numerical Methods Practical Questions.txt
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LIST OF PRACTICAL QUESTIONS:
1. Write a C program to calculate the Mean, Median and Mean Deviation of a simple distribution.
2. Write a C program to compute the Standard Deviation.
3. Write a C program to implement the Least Square Approximation for fitting a Straight line y=mx+c,
where "m" is the slope and "c" is the intercept on the y-axis for data points:
(-1,10), (0,9), (1,7), (2,5), (3,4), (4,3), (5,0), (6,-1).
4. Write a C program to find the real root of the equation Cube[x]-4x+1=0 by using the Method of Successive Approximation.
5. Write a C program to find a real root of the equation Square[x]-Sin[x]-9=0 by using the Bisection Method.
6. Write a C program to find a real root of the equation Sin[x]=1+Cube[x] correct to 3 decimal places by using the Newton-Raphson Method.
7. Write a C program to solve the following set of equations by Gauss Elimination Method:
2.x1 + 4.x2 + 2.x3 =15
2.x1 + x2 + 2.x3 = -54
x1 + x2 - 2.x3 = 0
8. Write a C program to solve the following set of equations by Gauss-Seidal Method:
27x + 6y - z = 85
6x + 15y + 2z = 72
x + y + 54z = 110
9. Write a C program to interpolate a function using Newton's Divided Difference Formula.
Use it to find the value of f(8). Given:
x: 4 5 7 10 11 12
f(x): 48 100 294 900 1210 2028
10. Write a C program to interpolate using Newton's Forward Interpolation Method.
Use it to find the value of y when x = 1.05. Given:
x: 1.0 1.1 1.2 1.3 1.4 1.5
y: 0.24197 0.21785 0.19419 0.17137 0.14973 0.12952
11. Write a C program to interpolate using Newton's Backward Interpolation Method.
Use it to find the value of y when x = 0.75. Given:
x: 0.0 0.2 0.4 0.6 0.8 1.0
y: 1.0 0.961538 0.833333 0.555556 0.3125 0.2
12. Write a C program to interpolate using Lagrange's Interpolation Method.
Use it to find the value of y when x = 6. Given:
x: 3 7 9 10
y: 168 120 72 63
13. Write a C program to evaluate Integrate[Divide[x,1+x],{x,0,1}] using Trapezoidal Rule.
14. Write a C program for integrating Simpson's One-Third Rule when the function values are given as:
x: 0.8 0.9 1.0 1.1 1.2
f(x): 0.71736 0.78333 0.84147 0.92314 0.96356
15. Write a C program to evaluate Integrate[Divide[x,1+Square[x]],{x,0,1}] using Simpson's One-Third Rule.
16. Write a C program to evaluate Integrate[Sqrt[1-8Power[x,3]],{x,0,0.3}] using Simpson's Three-Eight Rule.
17. Write a C program for solving a differential equation D[y=3x+Divide[y,2],x] and y(0)=1. Find the values of y(0,1) and y(0,2) by using the Taylor Series Method.
18. Write a C program for solving a differential equation D[y=Power[x,3]+y,x], y(0)=1.Find y(0,2) when h=0.01 by Euler's Method.
19. Write a C program for solving a differential equation D[y=Power[x,2]+y,x], y(0)=1.Find y(0.02) when h(0.01)=1 by Modified Euler's Method.
20. Write a C program to approximate y when x=0.1, 0.2, 0.3 and h=0.1 using Runge-Kutta Method. Given x=0, when y=1 and D[y,x]=x+y.