clc
clear all
xf = 10; % final time
y0 = 0; % initial value of y
yf = 100; % final value of y
%% define defferential equation
%- assume dy/dx = w
dy_dx =@(x,y,w) w;
dw_dx =@(x,y,w) 0.1*w - 0.05*y;
y(1,1) = y0;
% initial guess for w(0)
w(1,1) = (yf - y0)/(xf -0);
% solutin for first guess using euler method
h = 0.001; % stepsize
x = 0:h:xf;
for i = 1:length(x)-1
w(1,i+1) = w(1,i) + h*dw_dx(x(i),y(1,i),w(1,i));
y(1,i+1) = y(1,i) + h*dy_dx(x(i),y(1,i),w(1,i));
end
% second guess of w
w(2,1) = 3*(yf - y0)/(xf -0);
y(2,1) = y0; % remains same
% solution for second guess using euler method
for i = 1:length(x)-1
w(2,i+1) = w(2,i) + h*dw_dx(x(i),y(2,i),w(2,i));
y(2,i+1) = y(2,i) + h*dy_dx(x(i),y(2,i),w(2,i));
end
%% Refinement of solution using interpolation and further solution
using
% Euler method
% next guess of w using interpolation technique
w(3,1) = w(1,1) +
(yf-y(1,end))*(w(2,1)-w(1,1))/(y(2,end)-y(1,end));
y(3,1) = y0;
% Final solution using euler method
for i = 1:length(x)-1
w(3,i+1) = w(3,i) + h*dw_dx(x(i),y(3,i),w(3,i));
y(3,i+1) = y(3,i) + h*dy_dx(x(i),y(3,i),w(3,i));
end
%% Maximum value of y
ymax = max(y(end,1:end));
fprintf('\nMaximum value of y = %0.2f\n',ymax)
note:
thankyou:)
In Matlab please da? Solve the boundary value problem: 0.1-0.057 subject to the conditions:y(0)=0 and y(10)=100....
matlab code
Given the boundary value problem: daw = W 3 dw dc2 de w(x = 1) = 5 w(x = 10) = 5 Find the minimum value of wover this region using the shooting method. Round your answer to TWO decimal points rounding up for 5 or more. 0.55 0 -15.33 -0.55 10.25
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....
solution with matlab only please
Problem 2: Use the shooting method to solve d T _-10-7 (T +273)' + 4(150-7): 0 With the boundary conditions T(O)- 200 and T(0.5)-100
Problem 2: Use the shooting method to solve d T _-10-7 (T +273)' + 4(150-7): 0 With the boundary conditions T(O)- 200 and T(0.5)-100
please help
Problem 1: Solve the following differential equations subject to the specified boundary conditions: a. 40, subject to y(o) 30 and y(1) 10 br,subject to T(O2) 0 c. da-a29-0, (a is a constant), subject to θ(0) 50 and θ(x-.00) dx2 d20 dx? 10
Solve the boundary value problem $$ \begin{gathered} y^{\prime \prime \prime}=-\frac{1}{x} y^{\prime \prime}+\frac{1}{x^{2}} y^{\prime}+0.1\left(y^{\prime}\right)^{3} \\ y(1)=0 \quad y^{\prime \prime}(1)=0 \quad y(2)=1 \end{gathered} $$Use difference equations method. You can get help from matlab for solving the system.
2. The boundary value problem y" + ly = 0, y'(0)= 0 , y'(1) = 0) has normalized eigenfunctions 6(x)=1, 0,,(x) = V2 cos nix, n=1,2,3,... a. Using the method of eigenfunction expansion, solve the boundary value problem y " + 8y = x , y'(0)= 0, y'(1)=0 Set up, but do not evaluate, the required integrals. b. Determine how many solutions the below boundary value problem has. y" + 257² y = sinº 5ax , y(0) = 0 ,...
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....
Question 25 2 pts MATLAB's fminbnd function can be used to find the minimum value of a function of two independent variables. True False Question 26 5 pts Given the boundary value problem: du du dza w(x = 1) = 5 wx = 10) = 5 =W Find the minimum value of wover this region using the shooting method. Round your answer to TWO decimal points rounding up for 5 or more. 0.55 -15.33 -0.55 10.25
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?