f²uSet up the comparable problem using the first central difference approximation for , i.e. derive thefx²'arrays M and K in the system of equations represented bydx-+Kx=f(t), ⇒ x¹*¹ = x² − M¯¹[Kx + f(t¹)]AtdtThis is the implicit Euler algorithmM

The system of equations represented by the function fu can be set up using the comparable problem…

Answered: Set up the comparable problem using the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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x* – x – 1 = 0 i) Explain Secant algorithm. ii) Find positive root of the equation with error is less than 10-6 by Secant method for initial -9- interval [0,2] in MATLAB (or any other computation tool.) iii) Obtain the table which contains n, xn, f (xn),| xn – xn-1] values for each iteration step.
Consider the following interpolating points for the function f(x) = x² – 2x: Xi 01 23 f(xi) 0 -1 03 (a) Use monomial basis to find P₁(x) that interpolates f(x) at x; for i = 0,1. Con- struct the Vandermonde matrix and then use the backslash \ in matlab to solve the linear system. (b) Repeat (a) to find P₂(x) that interpolates f(x) at x; for i = 0, 1, 2. (c) Repeat (a) to find P3(x) that interpolates f(x) at x, for i = 0, 1, 2, 3. (d) Compare P₂(x), P3(x) and f(x). What do you see? Can you explain it?
we have an iterative algorithm where our first two approximations are r = 1 and Suppose 2 and each subsequent approximation is the average of the two previous approximations En0.5(r-+xn-2) for each n 2 3. Find the relative approximate error for r2, T3, and r4 i.e I2
4. (a) Compute A-¹ if A = (b) Use A-¹ to solve Ax = b, if b = (1, 1, 1)T. 10 3 2 3 4 2 3
Solve the following system using the Gaussian algorithm: 2x1 - x2 + 3x3 = 0 -2x1 + x2 - X3 = -2 x1 - 3x2 + 6x3 = 3 Let x be the vector x = |x2, where x1, x2 and x3 are solutions of the system, and y be the vector y =|1 Evaluate the scalar product of x and y. [Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer. So for example, if the correct answer is 6.78 then any input that lies between between 6.53 and 7.03 will be marked as correct.] Answer:
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Set up the comparable problem using the first central difference approximation for f²u fx² arrays M and K in the system of equations represented by dx -+Kx=f(t), ⇒ x¹*¹ = x² − M¯¹ [Kx + f(t¹)] At dt M This is the implicit Euler algorithm -, i.e. derive the