JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year NUMERICAL METHODS AND PARTIAL DIFFERENTIAL EQUATIONS Previous Question Paper (February - 2024 - R22)
Note: This question paper contains two parts A and B. Part- A for 10 marks, Part - B for 50 marks. Part-A is a compulsory question. Part-B consists of ten questions (numbered from 2 to 11) carrying 10 marks each. From each unit, there are two questions and the student should answer one of them. Hence, the student should answer five questions from Part-B.
Part A
What is the order of convergence of Newton-Raphson method?
Answer
The order of convergence of the Newton-Raphson method is 2 (quadratic convergence).
If A = LU then what is A-1?
Answer
If A = LU, then A-1 = U-1L-1.
Evaluate Δcos x.
Answer
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If f(x) values are known at unequal intervals of x, then which method is suitable to find an interpolating polynomial?
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To fit a curve of the form y = a + bx + cx2, by the method of least squares, write the normal equations.
Answer
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Write the normal equations to fit a curve of the form y = abx.
Answer
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Write Merits and Demerits of Taylor’s Series Method?
Answer
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Compare Trapezoidal rule and Simpson’s 1/3 rule?
Answer
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Find the differential equation of all spheres of fixed radius having their centre on the xy-plane.
Answer
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Solve z = px + qy + pq.
Answer
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Part B
Find the root of the equation x3 + x + 1 = 0 by Regular Falsi Method. Evaluate √12 by Newton Raphson method. Give the answer up to 4 decimal place of accuracy.
Answer
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Solve the system of equations by Gauss-Seidel iteration Method: 20x + y - 2z = 17; 3x + 20y - z = -18; 2x - 3y + 20z = 25.
Answer
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Estimate the population for 1895 using Newton’s forward difference formula for data: (1891, 46), (1901, 66), (1911, 81), (1921, 93), (1931, 101). Also find by Gauss’s Backward interpolating formula the value of y at x = 1936 given table: (1901, 12), (1911, 15), (1921, 20), (1931, 27), (1941, 39), (1951, 52).
Answer
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The following table gives the measurements of T made on curve recorded by the oscilograph representing a change of current I due to a change in conditions of an electric current. T: 1.2, 2, 2.5, 3; I: 1.36, 0.58, 0.34, 0.2. Find a polynomial T = f(x) using interpolation.
Answer
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Fit a straight line and a parabola to the following data and find out which one is most appropriate: (1,4), (2,3), (3,6), (4,7), (5,11).
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Fit a curve y = abx to the following data: x: 2, 3, 4, 5, 6; y: 144, 172.8, 207.4, 248.8, 298.5.
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Evaluate ∫ logx dx from 4 to 5.2 by using trapezoidal, Simpson’s 1/3, Simpson’s 3/8 rules for given data points.
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Find y(0.1) by Runge-Kutta method of 4th order for y' = x2 - y and y(0) = 1. Also, given y' = xy + y2, y(0) = 1, y(0.1) = 1.1169, y(0.2) = 1.2773, find y(0.3) by Milne’s Method.
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Solve p tanx + q tany = tanz and solve (p2 + x)2 + (q2 + y)2 = 1.
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Solve the partial differential equation p2x4 + y2zq = 2z2. Also solve by method of separation of variables ∂2U/∂x2 = ∂U/∂y + 2U.
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