Using Gauss-Seidel Method solve the following system:2х1 — бх, — хз — —38-3x1 – x2 + 7x3 = 34—8х1 + х2 — 2х3= 20Until the approximate error is less than 0.5% with the firstapproximations asX1 = -2,X2 =4,X3 = 3Round-off intermediate values to 6 decimal places and the answerto 4 decimal places.How many iterations were made to solve the system?NOTE: Please make the solution clear and readable.Give the full solution not in tabulated form, thank you!

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Answered: Using Gauss-Seidel Method solve 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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Solve the simultaneous, nonlinear equationsx1 ln x2 + x2 exp( x1) =ex(1)x2 ln x1+ 2x1 exp (x2) =2 exp(1)for x1 and x2 to within ± 0.001, by the Newton–Raphson method.
Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order: • Solve for k1 and k2. • Then, solve for the next value of y: for n = 1, 2, . . . where xn = x0 + nh. Now, try to solve the initial value problem y' = xy/(x2 + y2)1/2 with y(1) = 1 and h = 0.2 over the interval 1 ≤ x ≤ 2 using second-order Runge-Kutta Method. Solve the equation again by fourth-order Runge-Kutta Method and compare their results (i.e. 2nd order vs 4th order). Thank you
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 2x - 5y, x(0) = 2, y' = 4x - 2y, y(0) = 3; x(t) = 2cos 4t -11/4 sin 4t, y(t) = 3cos 4t + 1/2sin 4t
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = x + 2y, x(0) = 0,y' = 2x + y, y(0) = 2;x(t) = e3t - e-t , y(t) = e3t + e-t
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 3x + 4y, x(0) = 1, y' = 3x + 2y, y(0) = 1; x(t) = 1/7 (8e6t - e-t), y(t) =1/7(6e6t + e-t)
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = x -2y, x(0) = 0, y' = 2x + y, y(0) = 4; x(t) = -4et sin 2t, y(t) = 4et cos 2t
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 5x - 9y, x(0) = 0, y' = 2x - y, y(0) = -1; x(t) = 3e2t sin 3t, y(t) = e2t(sin 3t - cos 3t)
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 3x - y, x(0) = 2, y' = x + y, y(0) = 1; x(t) = (t+2) e2t, y(t) = (t+1) e2t
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 9x + 5y, x(0) = 1, y' = -6x - 2y, y(0) = 0; x(t) = -5e3t + 6e4t, y(t) = 6e3t + 6e4t
I want the solve of these equations using Gauss -Jordan Method
1. Solve the initial value problem y' = (3x2 + y2)1/2 − y with y(2) = 0 and h = 0.2 over the interval 2 ≤ x ≤ 3. Solve the equation again by analytical method and compare their results (i.e. analytical vs numerical).
Apply the Runge-Kutta method to approximate this solution on the interval [0, 0.5] with step size h=0.25. Show five-decimal-place values of the approximate solution and actual solution at the points x=0.25 and 0.5. y'=-3x2y, y(0)=6; y(x)=6e-x^3

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