CSC212 Numerical Method
Numerical Method: most repeated questions
Questions that have come up in more than one paper, matched by what they ask rather than exact wording. Most repeated first.
- 4×Asked in 2081, 2079, 2078, 2075Solve the following system of linear equations using Gauss Jordan elimination method. x+2y 3z=4 2x+4y 6z=8 x 2y+5z=4Answer coming5
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- Solve the following system of linear equations using Gauss Jordan elimination method. x+2y 3z=4 2x+4y 6z=8 x 2y+5z=4TU Board 2081
- Solve the following set of equations using Gauss Siedal method. x + 2y + 3z = 4 6x + 4y + 5z = 16 5x + 2y + 3z = 12TU Board 2079
- Solve the following set of linear equations using the Gauss Jordan method. x 2 + 2x 3 + 3x 4 = 9 7x 1 + 6x 2 + 5x 3 + 4x 4 = 33 8x 1 + 9x 2 + x 4 = 27 2x 1 + 5x 2 + 4x 3 + 3x 4 = 23TU Board 2078
- Solve the following set of equations using Gauss Seidel method. x + 2y + 3z = 4 6x – 4y + 5z = 10 5x + 2y + 2z = 25TU Board 2075
- 4×Asked in 2080, 2079, 2075, Model questionSolve the Poisson's equation ∇²f = xy and f=2 on boundary by assuming square domain 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 and h=1.Answer coming5
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- Solve the Poisson's equation ∇²f = xy and f=2 on boundary by assuming square domain 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 and h=1.TU Board 2080
- Solve the Poisson's equation ∇^2f=3x^2y over the square domain 0 ≤ x ≤ 3, 0 ≤ y ≤ 3 with f=0 on the boundary and h=1.TU Board 2079
- Solve the Poison's equation over the square domain 0 ≤ x ≤ 1.5, 0 ≤ y ≤ 1.5 with f = 0 on the boundary and h = 0.5.TU Board 2075
- Solve the Poison's equation over the square domain 0 ≤ x ≤ 1.5, 0 ≤ y ≤ 1.5 with f = 0 on the boundary and h = 0.5.Model question
- 3×Asked in 2079, 2075, Model questionEstimate the integral value of following function from x =1.2 to 2.4 using Simpson's 1/3 rule. x 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 f(x) 1.53 2.25 3.18 4.32 5.67 7.23 8.98 10.94 13.08Answer coming5
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- Estimate the integral value of following function from x =1.2 to 2.4 using Simpson's 1/3 rule. x 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 f(x) 1.53 2.25 3.18 4.32 5.67 7.23 8.98 10.94 13.08TU Board 2079
- Calculate the integral value of the function given below from x = 1.8 to x = 3.4 using Simpson's 1/3 rule. X 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4 F(x) 0.003 0.778 1.632 2.566 3.579 4.672 7.097 8.429TU Board 2075
- Calculate the integral value of the following tabulated function from x = 0 to x = 1.6 using simpson's 3/8 rule. x 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 f(x) 0 0.24 0.55 0.92 1.63 1.84 2.37 2.95 3.56Model question
- 3×Asked in 2080, 2077, Model questionConstruct Newton's backward difference table for given data points and approximate the value of f(x) at x=45. x 10 20 30 40 50 f(x) 0.985 0.934 0.866 0.766 0.643Answer coming5
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- Construct Newton's backward difference table for given data points and approximate the value of f(x) at x=45. x 10 20 30 40 50 f(x) 0.985 0.934 0.866 0.766 0.643TU Board 2080
- Construct Newton's forward difference table for the given data points and approximate the value of f(x) at x = 15. x 10 20 30 40 50 F(x) 0.173 0.342 0.5 0.643 0.766TU Board 2077
- Construct Newton's forward difference table for the given data points and approximate the value of f(x) at x = 12. x 10 20 30 40 50 F(x) 0.173 0.342 0.5 0.643 0.766Model question
- 3×Asked in 2080, 2077, Model questionHow secant methods differs from Newton Rhapson method? Derive the formula for Secant Method. Solve the equation Cosx + 2Sinx – x² = 0 using Secant method. Assume error precision as 0.01. Discuss the drawbacks of the Newton Rhapson method.Answer coming10
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- How secant methods differs from Newton Rhapson method? Derive the formula for Secant Method. Solve the equation Cosx + 2Sinx – x² = 0 using Secant method. Assume error precision as 0.01. Discuss the…TU Board 2080
- Derive the formula for Newton Raphson Method. Solve the equation x^2 + 4x – 9 = 0 using Newton Raphson method. Assume error precision is 0.01. Discuss drawbacks of the Newton Raphson method.TU Board 2077
- Derive the formula for Newton Raphson method. Solve the equation x^4 – x – 10 = 0 using Newton Raphson method assuming error precision is 0.01. Discuss drawback for this method.Model question
- 3×Asked in 2078, 2075, Model questionEvaluate the following integration using Romberg integration. 0^1 sin^2 xx dxAnswer coming5
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- 3×Asked in 2080, 2077, Model questionFit the quadratic curve through the following data points and estimate the value of f(x) at x=2. x 1 3 4 5 6 y 2 7 8 7 5Answer coming5
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- Fit the quadratic curve through the following data points and estimate the value of f(x) at x=2. x 1 3 4 5 6 y 2 7 8 7 5TU Board 2080
- Fit the curve y = ae^bx through the following data points. x 1 2 3 4 y 1.65 2.70 4.50 7.35TU Board 2077
- Fit the curve y = ae^bx through the following data points. x 0 1 3 5 7 9 y 1.0 0.891 0.708 0.563 0.447 0.355Model question
- 3×Asked in 2077, 2075, Model questionHow boundary value problems differs from initial value problems? Discuss shooting method for solving boundary value problem.Answer coming5
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- How boundary value problems differs from initial value problems? Discuss shooting method for solving boundary value problem.TU Board 2077
- What is initial value problem and boundary value problem? Write an algorithm and program to solve the boundary value problem using shooting method.TU Board 2075
- Solve a boundary value problem by using shooting method d^2ydx^2 = 6x , y(1) = 2, y(2) = 9Model question
- 3×Asked in 2080, 2077, Model questionHow Gauss Jordan method differs from Gauss Elimination method? Solve the following system of equations using Gauss Jordan method. How can we use Gauss Jordan method to find the inverse of a matrix? Discuss. 2x – y + 4z = 15 2x + 3y – 2z = 4 3x + 2y – 4z = 4Answer coming10
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- How Gauss Jordan method differs from Gauss Elimination method? Solve the following system of equations using Gauss Jordan method. How can we use Gauss Jordan method to find the inverse of a matrix?…TU Board 2080
- Why partial pivoting is used with Naive Gauss Elimination method? Solve the following system of equations using Gauss Elimination method with partial pivoting? How Gauss Jordan method differs from…TU Board 2077
- Why partial pivoting is used with Naive Gauss Elimination method? Solve the following system of equations using Gauss Elimination method with partial pivoting? How Gauss Jordan method differs from…Model question
- 3×Asked in 2080, 2079, Model questionWrite down the program for solving ordinary differential equation using Heun's method.Answer coming5
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- 2×Asked in 2077, Model questionA plate of dimension 18cm x 18cm is subjected to temperatures as follows: left side at 100^0c , right side at 200^0c . Upper part at 50^0c , and lower at 150^0c . If square grid length of 6cm x 6cm is assumed, what will be the temperature at the interior…Answer coming5
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- A plate of dimension 18cm x 18cm is subjected to temperatures as follows: left side at 100^0c , right side at 200^0c . Upper part at 50^0c , and lower at 150^0c . If square grid length of 6cm x 6cm…TU Board 2077
- A plate of dimension 18cm x 18cm is subjected to temperatures as follows: left side at 100^0c , right side at 200^0c . Upper part at 50^0c , and lower at 150^0c . If square grid length of 6cm x 6cm…Model question
- 2×Asked in 2077, Model questionHow interpolation differs from regression? Write down algorithm and program for Lagrange interpolation.Answer coming10
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- 2×Asked in 2077, Model questionHow Simpson's 1/3 rule differs from Trapezoidal rule? Drive the formula for Simson's 1/3 rule.Answer coming5
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- 2×Asked in 2079, 2078Solve the following differential equation for 0 ≤ x ≤ 1 taking h=0.5 using Runge Kutta 4th order method. y'(x) + y = 3x with y(0)=2Answer coming5
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- 2×Asked in 2078, 2075Write matrix factorization? How can be used to solve a system of linear equations? Factorize the given matrix A and solve the system of equations Ax = b for given b using L and U matrices. A = bmatrix1 & 2 & 3\\ 2 & 8 & 11\\ 3 & 22 & 36 bmatrix and b =…Answer coming10
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- Write matrix factorization? How can be used to solve a system of linear equations? Factorize the given matrix A and solve the system of equations Ax = b for given b using L and U matrices. A =…TU Board 2078
- What is matrix factorization? Factorize the given matrix A into LU using Doolittle algorithm and also solve Ax = b for given b using L and U matrices. A = bmatrix2 & 4 & 4 & 0\\ 1 & 5 & 5 & 3\\ 2 &…TU Board 2075