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How do I solve this problem? Problem 3 For the following differential equation, construct a finite...
solve using matlab or by hand. For the following differential equation, answer the questions. -y"+y=x (0.0 SX 35.0) y(0.0)=1.0, y(5.0)= 2.0 (1) Solve the differential equation analytically. (2) Solve the differential equation using centered finite difference approximation of y" with a step size of 1.0 and check the accuracy of the solutions.
Write a MATLAB code to solve below 2nd order linear ordinary differential equation by finite difference method: y"-y'-0 in domain (-1, 1) with boundary condition y(x-1)--1 and y(x-1)-1. with boundary condition y an Use 2nd order approximation, i.e. O(dx2), and dx-0.05 to obtain numerical solution. Then plot the numerical solution as scattered markers together wi exp(2)-explx+1) as a continuous curve. Please add legend in your plot th the analytical solution y-1+ Write a MATLAB code to solve below 2nd order...
NOTE: h=(b - a) / N Consider the differential equation y" y' +2y + cos(), for 0 x , with boundary conditions (0) 0.3, Show that the exact solution is (x)(sin3 cos())/10. (a). Consider a uniform grid with h (b? a)/N. Set up the finite difference method for the problem. Write out this tri-diagonal system of linear equations for yi, (b). Write a Matlab program that computes the approximate solution yi. You may either use the Matlab solver to solve...
Assignment 2 Q.1 Find the numerical solution of system of differential equation y" =t+2y + y', y(0)=0, at x = 0.2 and step length h=0.2 by Modified Euler method y'0)=1 Q.2. Write the formula of the PDE Uxx + 3y = x + 4 by finite difference Method . Q.3. Solve the initial value problem by Runga - Kutta method (order 4): y" + y' – 6y = sinx ; y(0) = 1 ; y'(0) = 0 at x =...
Project Being able to analytically calculate the solution to a given partial differential equation is often a much more difficult (if not impossible) task than presented here. Possible challenges include irregular domains and strange numerical techniques are often used to approximate the solution to a PDE. The most basic of such methods is the finite difference method. To illustrate the method, consider the Dirchlet Poisson equation in one dimension given by 10:Finite Difference Approximation ary conditions. In those cases, The...
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...
QUESTION 9 Consider given ordinary differential equation, y"+y" - 2y = 0, y(t = 0) = 0, y'(t = 0) = 1. What is the y at t= 0.2 when the equation is solved using finite difference method with At = 0.12 Use central difference approximation for y" and y'. Note: to receive the credit, the final numeric answer MUST be within the range of plus/minus 0.02. Use the 4 significant digits for the step-by-step calculation and final answer, i.e.,...
Consider the following initial value problem у(0) — 0. у%3D х+ у, (i) Solve the differential equation above in tabular form with h= 0.2 to approximate the solution at x=1 by using Euler's method. Give your answer accurate to 4 decimal places. Given the exact solution of the differential equation above is y= e-x-1. Calculate (ii) all the error and percentage of relative error between the exact and the approximate y values for each of values in (i) 0.2 0.4...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
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,...