Given the following non-linear boundary value problem Use the shooting method to approximate solution Use finite...
Please provide the program in Matlab. Question 12) Solve the boundary value problem using a program/script that applied the shooting method. (t) + y()-8 with the boundary conditions of y(0)-0 and y(10-0. Use ΔΧ-1. Plot on the same axis your solution and the exact solution dt2 t 4 4 dt Question 12) Solve the boundary value problem using a program/script that applied the shooting method. (t) + y()-8 with the boundary conditions of y(0)-0 and y(10-0. Use ΔΧ-1. Plot on...
Set up and solve a boundary value problem using the shooting method using Matlab A heated rod with a uniform heat source may be modeled with Poisson equation. The boundary conditions are T(x = 0) = 40 and T(x = 10) = 200 dTf(x) Use the guess values shown below. zg linspace (-200,100,1000); xin-0:0.01:10 a) Solve using the shooting method with f(x) = 25 . Name your final solution "TA" b) Solve using the shooting method with f(x)-0.12x3-2.4x2 + 12x....
Consider the following boundary-value problem$$ y^{\prime \prime}-2 y^{\prime}+y=x^{2}-1, y(0)=2, \quad y(1)=4 $$Apply the linear shooting method and the Euler method with step size of \(\frac{1}{3}\) to marks) approximate the solution of the problem.
MATH LAB CODE PLS ter Problems 1. Use finite differences to approximate solutions to the linear BVPs for n=9, 19, and 39. (a) | y" = y + ſet { y(0) = 0) 1 y(1) = ſe (b) | y" = (2 + 442) y { y(0) = 1 y(1) = e Plot the approximate solutions together with the exact solutions (a) y(t) = te'/3 and (b) y(t) = et', and display the errors as a function of t in...
03. Consider the boundary value problem 0 Sts1 y(0) & y(1)-1 where k > 0 is a given real parameter a. Verify that y(t) = e-kt (14) is the exact solution of the BVP. b. Use the function mybvp() from the previous problem with h -0.1 and k -10, to solve the BVP by the Finite Difference Method. Plot, on the same axes, the numerical and exact solution. c. Using a log-log plot, graph the maximum error as a function...
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)...
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...
2. Use an RK4 shooting method with a step size of h - 0.01 to find the unique negative solution to the boundary value problem non ul") -u)- 05 x 1 u(0)0, u(1) - 1 1 + x Hi Then give the approximate value of u(0.5 2. Use an RK4 shooting method with a step size of h - 0.01 to find the unique negative solution to the boundary value problem non ul") -u)- 05 x 1 u(0)0, u(1) -...
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...
Given the following two point boundary value problem: ty" + 2y + (3 - t)y = 4, y(2) = -1, y(8) = 1. Divide the given interval (3.7] into three equal sub-intervals, and apply the finite difference method (i,e: use the formulas for approximating y' and y" derive from Taylor series erpansion) to SETUP ( do not solve) a system of linear equations (write it in "A.r = b" form that will allow you to approximate the function value of...