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Nepathya College Mid Term Exam 2072 Bachelor Level/Third Semester Full Marks: 40 CSC-204 Pass Marks: 12 Numerical Method Time: 1:30 Attempt any five questions. (5*8=40) 1. Write the algorithm of NR method. Find the positive root of equation F(x) =cos x-1.3x by using bisection method. 2. Define interpolation. Estimate the value of f(2.5) using cubic spline. i 0 1 2 3 X i 1 2 3 4 F(x i ) 0.5 0.3333 0.25 0.2 3. Use gauss quadrature formula for n=3 evaluate ∫ 0 1 dx ( 1 + x 2 ) 4. How gauss elimination method can solve the any system equation. Solve the following system of equation by applying Gauss- Seidel method . Carry out the iterations up to 6 th stage. 28x+4y-z=32 X+3y+10z=24 2x+17y+4z=35 5. Derive the expression for Laplace equation. Solve the equation ∇ 2 u=-10(x 2 +y 2 +10) over the boundary mesh with sides x=0, y=0 and x=3, y=3 with u = 0 on the boundary and mesh length h=1. 6. Write the c-program to illustrate the NR method.

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Nepathya CollegeMid Term Exam

2072Bachelor Level/Third Semester Full Marks: 40 CSC-204 Pass Marks: 12Numerical Method Time: 1:30

Attempt any five questions. (5*8=40)1. Write the algorithm of NR method. Find the positive root

of equation F(x) =cos x-1.3x by using bisection method.

2. Define interpolation. Estimate the value of f(2.5) using cubic spline.

i 0 1 2 3Xi 1 2 3 4

F(xi) 0.5 0.3333 0.25 0.2

3. Use gauss quadrature formula for n=3 evaluate ∫0

1 dx(1+x2)

4. How gauss elimination method can solve the any system equation. Solve the following system of equation by applying Gauss- Seidel method . Carry out the iterations up to 6th stage.

28x+4y-z=32X+3y+10z=242x+17y+4z=35

5. Derive the expression for Laplace equation. Solve the equation ∇2u=-10(x2+y2+10) over the boundary mesh with sides x=0, y=0 and x=3, y=3 with u = 0 on the boundary and mesh length h=1.

6. Write the c-program to illustrate the NR method.

Nepathya CollegeMid Term Exam

2072Bachelor Level/Third Semester Full Marks: 40 CSC-204 Pass Marks: 12Numerical Method Time: 1:30

Attempt any five questions. (5*8=40)1. Write the algorithm of NR method. Find the positive root

of equation F(x) =cos x-1.3x by using bisection method.

2. Define interpolation. Estimate the value of f(2.5) using cubic spline.

I 0 1 2 3Xi 1 2 3 4

F(xi) 0.5 0.3333 0.25 0.2

3. Use gauss quadrature formula for n=3 evaluate ∫0

1 dx(1+x2)

4. How gauss elimination method can solve the any system equation. Solve the following system of equation by applying Gauss- Seidel method . Carry out the iterations up to 6th stage.

28x+4y-z=32X+3y+10z=242x+17y+4z=35

5. Derive the expression for Laplace equation. Solve the equation ∇2u=-10(x2+y2+10) over the boundary mesh with sides x=0, y=0 and x=3, y=3 with u = 0 on the boundary and mesh length h=1.

6. Write the c-program to illustrate the NR method.


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