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Use the Gauss-Seidel method to solve the following system until the percent relative error falls below
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- Use 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_forwardFor the following system, perform only the first elimination using Gaussian Elimination with partial pivoting.arrow_forward4. Solve the 2D Laplace's equation on a square domain using finite difference method based on central differences with error O(h2). Use four nodes in each direction. 0 (1.y)--5 (2.1) 0arrow_forward
- 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_forward2. Solve the following ODE in space using finite difference method based on central differences with error O(h). Use a five node grid. 4u" - 25u0 (0)=0 (1)=2 Solve analytically and compare the solution values at the nodes.arrow_forwardUse the Lax method to solve the inviscid Burgers' equation using a mesh with 51 points in the x direction. Solve this equation for a right propagating discontinu- ity with initial data u = 1 on the first 11 mesh points and u = 0 at all other points. Repeat your calculations for Courant numbers of 1.0, 0.6, and 0.3 and compare your numerical solutions with the analytical solution at the same time.arrow_forward
- Look at the two imagesarrow_forwardDIna Sami h.w1: solve the following differential equation numerically using Runge-Kutta Method (4th order). Find y (0.5) when y = 2 x + y, y (0) = 1. Take h = 0.5 boiker 00arrow_forward3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(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_forward
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning