✅ Numerical Methods

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📜Practical Questions

Q1)   Write a C program to calculate the Mean, Median and Mean Deviation of a simple distribution.

• See Solution✅

Q2)   Write a C program to compute the Standard Deviation.

• See Solution✅

Q3)   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)

• See Solution✅

Q4)   Write a C program to find the real root of the equation x³-4x+1 = 0 by using the Method of Successive Approximation.

• See Solution✅

Q5)   Write a C program to find a real root of the equation x²-sin(x)-9 = 0 by using the Bisection Method.

• See Solution✅

Q6)   Write a C program to find a root of the equation x²-25 = 0 by using the Regula-False Method.

• See Solution✅

Q7)   Write a C program to find a real root of the equation sin(x) = 1+x³ correct to 3 decimal places by using the Newton-Raphson Method.

• See Solution✅

Q8)   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

• See Solution✅

Q9)   Write a C program to solve the following set of equations by Gauss-Seidel Method:

27x + 6y - z = 85
6x + 15y + 2z = 72
x + y + 54z = 110	

• See Solution✅

Q10)   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

• See Solution✅

Q11)   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	

• See Solution✅

Q12)   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

• See Solution✅

Q13)   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		

• See Solution✅

Q14)   Write a C program to evaluate the following using Trapezoidal Rule.

• See Solution✅

Q15)   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

• See Solution✅

Q16)   Write a C program to evaluate the following using Simpson's One-Third Rule.

• See Solution✅

Q17)   Write a C program to evaluate the following using Simpson's Three-Eighth Rule.

• See Solution✅

Q18)   Write a C program for solving a differential equation

and y(0)=1. Find the values of y(0,1) and y(0,2) by using the Taylor Series Method.

• See Solution✅

Q19)   Write a C program for solving a differential equation

and y(0)=1. Find y(0,2) when h=0.01 by Euler's Method.

• See Solution✅

Q20)   Write a C program for solving a differential equation

and y(0)=1. Find y(0.02) when h=0.01 by Modified Euler's Method.

• See Solution✅

Q21)   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 f(y,x)=x+y.

• See Solution✅

Q22)   Huen's Method.

• See Solution✅

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