Known transport equation:
Make a finite difference scheme for the above transport equation
using the method:
Backward Time Backward Space
Known transport equation: Make a finite difference scheme for the above transport equation using the method:...
(Reference: Computer Aided Engineering) QUESTION 0.1 Use centered difference for time and centered difference for space to determine the explicit finite difference scheme for 2-D wave equation given below. Use index i for space, and index n for time. Un = Uxx QUESTION NO.2 Use forward difference for time and backward difference for space to find out the explict finite difference scheme for 1-D wave equation given below. Use index for space, and index n tor tme (Reference: Computer Aided...
Need help solving it using matlab with for loop Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
Consider the following boundary value problem: du du dx dx u=-e* sin(x) Discretize the ODE using backward second-order accurate scheme for both derivatives. The second order finite accuracy difference for the derivatives are given by: 2h (3)-1(1,2)-45 (7.1)+31(x) 8 (*)== (4.5) +41 (1.2) -51 (3.1) +2f (x) h?
Question 25 1 pts Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA (c) a + 2 = L(x) * € (0,L] B.C's: u (0) = 0 and EA (x) din le=L= F. An appropriate algebraic equation to use in the finite difference of the boundary condition at = Lis There is no suitable finite difference equation that can be obtained. u(L) - u (L - Ax) F.A BAL) None of...
Problem 1 (Section 6.3) Starting with the finite difference expressions for the partial derivatives, re-derive the forward Euler method for the heat equation with an extra nonlinear term: u(0,t)- u(1t)-0 Then, find the solution over three time steps (i.e. find the twelve vawith 3 decimal digits of precision, assuming k = 1, γ=2, M = 0.01, L = 1 and N=5, with initial condition u a table to show your results. It is strongly recommended that you write a short...
Problem 4: Suppose that the movement of rush-hour traffic on a typical expresswa be modeled using the differential equation du du where u(x) is the density of cars (vehicles per mile), and a is distance miles) in the direction of traffic flow. We w to the boundary conditions ant to solve this equation subject u(0) 300, u(5) 400. a) Use second-order accurate, central-difference approximations to discretize the differential equation and write down the finite-difference equation for a typical point zi...
For the following set of data, calculate the derivative using the higher order finite-difference approximations for each data point, as shown in Figures 21.43-21.5. Round your answers to 2 decimal places, if needed. 0 0.5 1.0 1.5 2.0 2.5 X f(x) 33 72 80 10 25 58 Using the forward finite-difference approximation: f'(0) ~ f'(0.5) Using the centered finite-difference approximation: f'(1.0) f'(1.5) Using the backward finite-difference approximation: f'(2.0) f'(2.5) 은 8
Question 19 Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA () 9 + - =D () 2 € (0,L] B.C's:u (0) = 0 and EA (2) --=F. An appropriate algebraic equation to use in the finite difference solution of the boundary value problem posed in question 24 is -Post A)u(L) - (L+Ax) EAL) F. 201 B) Su (L) - u(L - Ax) + 4u (L + A2) EAL C) (L)...
Derive the W-Momentum equation using the finite volume method. Show the derivation in 2D using W and U.
Construct the weak form and the finite element model of the following differential equation over a typical element Ω0€ (rf.xs). d ( du〉 , du dx dx)d Here a, b, and fare known functions of x and u is the dependent variable. The natural boundary conditions should not involve the function b(r). Construct the weak form and the finite element model of the following differential equation over a typical element Ω0€ (rf.xs). d ( du〉 , du dx dx)d Here...