for next parts data from previous question not available .
03. Consider the boundary value problem 0 Sts1 y(0) & y(1)-1 where k > 0 is a given real paramete...
(16 pts) Given boundary value problem (1 - 2)y" + 2xy' = 1 y(0) = 0, y'(1) = 0 (a) (6 pts) yı = 1 is a solution to homogeneous equation (1 – 22)y" + 2xy' = 0, find a second solution y2 by reduction of order method. (b) (6 pts) Find Green's function G (1, t) of the BVP. (c) (4 pts) Find a solution of the BVP using G (2,t).
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.) Problem 11. 12 marks] Consider the following two-point...
Consider the following initial value problem y = -5y + 5++ 2t, Ostsi, y(0) = 1/3, with h = 0.1. The exact solution of this problem is y(t) = {2 + e-5t. (2) If you use 2-step Adams-Moulton method (AM2) to solve this problem, what is the specific formula expressing Yi+1 in terms of Yi, Yi-1, të+1, ti, and ti-1 for solving this problem? (3) Use 2-step Adams-Moulton method (AM2) to solve this problem and plot the results to compare...
use Matlab y'=t, y0)=1, solution: y(t)=1+t/2 y' = 2(1 +1)y, y(0)=1, solution: y(t) = +24 v=5"y, y(0)=1, solution: y(t) = { y'=+/yº, y(0)=1, solution: y(t) = (31/4+1)1/3 For the IVPs above, make a log-log plot of the error of Runge-Kutta 4th order at t=1 as a function of h with h=0.1 x 2-k for 0 <k <5.
please use matlab to solve Problem # 3 P-3 Flow between two paralle plates is described by the following equation dith boundary conditons given as u,-0 & u,-o Calculate the velocity profile using the shooting method for solving the given BVP and compare your results by plotting the numerical solution over the plot of the analytical solution described by: (y-F )where ğr--0000025.H-О75 and h,30 Hint: use 1.75 for the first initial slope, and the other one is 0.45 to 0.5....
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...
Project. Solve the boundary-value problem: y(1)0 10 Verify that your solution y(x) satisfies the differential equation at every point in (-1,1). Is y twice differentiable at all points in (-1,1)1? Project. Solve the boundary-value problem: y(1)0 10 Verify that your solution y(x) satisfies the differential equation at every point in (-1,1). Is y twice differentiable at all points in (-1,1)1?
Question 1: Given the initial-value problem 12-21 0 <1 <1, y(0) = 1, 12+10 with exact solution v(t) = 2t +1 t2 + 1 a. Use Euler's method with h = 0.1 to approximate the solution of y b. Calculate the error bound and compare the actual error at each step to the error bound. c. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual value...
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...
Consider the initial value problem y' +y=e-, with y(0) = 0. PROJECT 1.) Find the exact solution to this equation, say 0(x). 2.) Use MATLAB to plot 6(x) in the interval [0.0, 4.0] . Use sufficient points to obtain a smooth curve. 3.) Now create a MATLAB program that uses Euler's Method to approximate the values of $(2) at N = 10 equally spaced points in (0,4). Plot these points on the same plot that was generated in part 2....