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Solve the following initial-value problem over the intervalfrom
Use the non-self-starting Heun method with a step size of 0.5 and initial conditions of
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Chapter 26 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- A root of the function f(x) = x3 – 10x² +5 lies close to x = 0.7. Doing three iterations, compute this root using the Newton- Raphson method with an initial guess of x=1). Newton-Raphson iterative equation is given as: f(x;) Xi+1 = Xị - f'(xi)arrow_forwardx^2-5x^(1/3)+1=0 Has a root between 2 and 2.5 use bisection method to three iterations by hand.arrow_forwardGiven the data below: Xo = 1 X1= 2 x2 = 4 Axo) = 2 Ax1) = 3 Ax2 : = 8 (i) Calculate the second-order interpolating polynomial using the method of the Newton's interpolating polynomial. (ii) Use the interpolating polynomial in (i) to calculate the approximated/interpolated functional value at x = 3, i.e., (3). (iii)Calculate the percentage relative error if the true value of f(3) is 4.8.arrow_forward
- Solve the following initial value problem by the method of Laplace Transformarrow_forwardApproximate solution of the initial value problem up to 3rd order using the Taylor series method. find it.arrow_forwardUse the graphical method to find the optimal solution for the following LP equations: Min Z=10 X1 + 25 X2 Subject to X1220, X2 ≤40 ,XI +X2 ≥ 50 X1, X2 ≥ 0.arrow_forward
- 8. Use the Lagrange multiplier method to find the point on the line 3x + 8y = 146 that is closest to the origin.arrow_forwardQ1 / Reduce the block diagram to the simple form R(s) S 13 S 0. S 1 S C(s)arrow_forwardThe values of p and h which renders (makes) the following set of equations dynamically and statically decoupled are, respectively. k,+k2 5 p+4 x1 = 0, X2 7 h+1 + [7h+1 J+e 5 p+4 J+e h= -0.214 and p = -1.76 h = -0.143 and p= -0.8 h = -0.281 and p= -1.2 h = -0.081 and p = -0.536arrow_forward
- 2- (Initial Value Problem in the Case of a Double Root) Solve the initial value problem y"+y+0.25y = 0, y(0) = 3.0, y' (0) = -3.5.arrow_forward3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0arrow_forwardProblem1: Solve the system of linear equations by each of the methods listed below. (a) Gaussian elimination with back-substitution (b) Gauss-Jordan elimination (c) Cramer's Rule 3x, + 3x, + 5x, = 1 3x, + 5x, + 9x3 = 2 5x, + 9x, + 17x, = 4arrow_forward
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