Consider the following boundary value problem: du du dx dx u=-e* sin(x) Discretize the ODE using...
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...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
solve problem #1 depending on the given information Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
Question about MATLAB boundary value problem. How can I solve the following problems? I would appreciate if you could briefly explain how you get the answer. (In the second problem, the selected answer is not correct.) Given the differential equation: u" + 2u' - xu = 0 subject to the boundary conditions: du/dx (x = 0) = 4 u(x = 5) = 10 This is to be solved using a second-order accurate in space method with x = 0.1. Which...
Consider the second order partial differential equation du/dt= d^2u/dx^2 +2du/dx+u over the domain x in [0,l) and t>=0. It is given that u(0,t)=u(l,t)=0. Use the method of separation of variables to prove that the general solution with the given boundary condition is u(x,t)= infinity series n=1 bnsin(npix/l)exp(-x-((npi/l)^2)t) where bn is a constant for every n N Hint u(x,t)=X(x)T(t) tnsit te Seind ond partial difertinl cuatan +2n St the dowain e To,e) an Use metod o Separet ion Vaiades to rore...
use matlab only please Problem # 1 P-1 Solve the following initial value problem using a4 order RK scheme: dy dx=tan(x), y(0)= 0.0 - Compare your results by calcudating the error andploting with the equation analytical solution y = In Isec(x)| for a = 0 to b = π/4 and step size 0.01 π: b- Solve the same problem with an accurate library scheme that can improve the answer 03 03 07 Problem # 1 P-1 Solve the following initial...