IGNOU BCSL 57 SOLVED ASSIGNMENT

Ques 1.

Write a program in C that accepts a decimal number and displays its floating-point equivalent number. You may make assumptions to simplify the program, however, your representation of floating point number should be closer to IEEE 754 standard 32 bit representation.

Ques 2.

 Write a program in C to implement Regula-Falsi method.

Ques 3.

Write a program to implement Gauss Elimination method for solving linear equations. Your method should check if a given pivot is zero or not. It should also minimise the floating-point errors.

Ques 4.

4. Write a program in C for the demonstration of Stirling's Formula for Interpolation. (5 Marks)
Q5. Write a C Program for solving the following system of equations using Jacobi method:
```

```
Starting with x^(0) = (0, 0, 0, 0). The exact solution is x = (1, 2, 3, 4)ᵀ. 

Ques 5.

Write a C program to solve the IVP y' = -ty², y(2) = 1 and find y(2.1) and y(2.2) with h = 0.1 using improved tangent method (modified Euler method) of O(h²). 

Ques 6.

Write a C program to solve the IVP y' = -ty², y(2) = 1 and find y(2.1) and y(2.2) with h = 0.1 using improved tangent method (modified Euler method) of O(h²). (5

Ques 7.

 Write a program in C to solve the equation x²y' = 1-xy-x², y(1) = -1 from x=1 to x=2 by using Taylor series method of O(h²) with h= 1/3 and ¼ and find the actual error at x=2 if the exact solution is y=-1/x .

Ques 8.

Write a program in C that accepts a decimal number and displays its floating-point equivalent number. You may make assumptions to simplify the program, however, your representation of floating point number should be closer to IEEE 754 standard 32 bit representation.

Ques 9.

 Write a program in C to implement Regula-Falsi method.

Ques 10.

Write a program to implement Gauss Elimination method for solving linear equations. Your method should check if a given pivot is zero or not. It should also minimise the floating-point errors.

Ques 11.

4. Write a program in C for the demonstration of Stirling's Formula for Interpolation. (5 Marks)
Q5. Write a C Program for solving the following system of equations using Jacobi method:
```

```
Starting with x^(0) = (0, 0, 0, 0). The exact solution is x = (1, 2, 3, 4)ᵀ. 

Ques 12.

Write a C program to solve the IVP y' = -ty², y(2) = 1 and find y(2.1) and y(2.2) with h = 0.1 using improved tangent method (modified Euler method) of O(h²). 

Ques 13.

Write a C program to solve the IVP y' = -ty², y(2) = 1 and find y(2.1) and y(2.2) with h = 0.1 using improved tangent method (modified Euler method) of O(h²). (5

Ques 14.

 Write a program in C to solve the equation x²y' = 1-xy-x², y(1) = -1 from x=1 to x=2 by using Taylor series method of O(h²) with h= 1/3 and ¼ and find the actual error at x=2 if the exact solution is y=-1/x .

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