💻 Numerical Methods

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📜List of Practical Questions:

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

• See the Solution ✅

• See the Output 🖥

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

• See the Solution ✅

• See the Output 🖥

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 the Solution ✅

• See the Output 🖥

Q4)   Write a C program to find the real root of the equation by using the Method of Successive Approximation.

$$ {x^3-4x+1=0} $$

• See the Solution ✅

• See the Output 🖥

Q5)   Write a C program to find a real root of the equation by using the Bisection Method.

$$ {x^2-sinx-9=0} $$

• See the Solution ✅

• See the Output 🖥

Q6)   Write a C program to find a real root of the equation correct to 3 decimal places by using the Newton-Raphson Method.

$$ {sinx=1+x^3} $$

• See the Solution ✅

• See the Output 🖥

Q7)   Write a C program to solve the following set of equations by Gauss Elimination Method:

2x₁ + 4x₂ + 2x₃ = 15
2x₁ + x₂ + 2x₃ = -54
x₁ + x₂ - 2x₃ = 0

• See the Solution ✅

• See the Output 🖥

Q8)   Write a C program to solve the following set of equations by Gauss-Seidal Method:

$$ {27x + 6y - z = 85} $$

$$ {6x + 15y + 2z = 72} $$

$$ {x + y + 54z = 110} $$

• See the Solution ✅

• See the Output 🖥

Q9)   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 the Solution ✅

• See the Output 🖥

Q10)   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 
f(x):	0.24197		0.21785		0.19419		0.17137		0.14973		0.12952 

• See the Solution ✅

• See the Output 🖥

Q11)   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 
f(x):	 1.0	   0.961538	  0.833333	0.555556	0.3125		0.2 

• See the Solution ✅

• See the Output 🖥

Q12)   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
f(x):	168	120	72	63 

• See the Solution ✅

• See the Output 🖥

Q13)   Write a C program to evaluate using Trapezoidal Rule.

$$\int_{0}^{1}\frac{x}{1+x}\ dx$$

• See the Solution ✅

• See the Output 🖥

Q14)   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 the Solution ✅

• See the Output 🖥

Q15)   Write a C program to evaluate using Simpson's One-Third Rule.

$$\int_{0}^{1}\frac{x}{1+x^2}\ dx$$

• See the Solution ✅

• See the Output 🖥

Q16)   Write a C program to evaluate using Simpson's Three-Eight Rule.

$$\int_{0}^{0.3}\sqrt{1-8x^3}\ dx$$

• See the Solution ✅

• See the Output 🖥

Q17)   Write a C program for solving the differential equation where y(0)=1. Find the values of y(0, 1) and y(0, 2) by using the Taylor Series Method.

$$\frac{dy}{dx}=3x+\frac{y}{2}$$

• See the Solution ✅

• See the Output 🖥

Q18)   Write a C program for solving the differential equation where y(0)=1. Find y(0, 2) when h = 0.01 by Euler's Method.

$$\frac{dy}{dx}=x^3+{y}$$

• See the Solution ✅

• See the Output 🖥

Q19)   Write a C program for solving the differential equation where y(0)=1. Find y(0.02) when h(0.01) = 1 by Modified Euler's Method.

$$\frac{dy}{dx}=x^2+{y}$$

• See the Solution ✅

• See the Output 🖥

Q20)   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

$$\frac{dy}{dx}=x+{y}$$

• See the Solution ✅

• See the Output 🖥

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Made by Kaustav Purkayastha😉