![Jsersleskandara\Desktop\New folder (7leuler.m* PUBLI.. VIEW 2 VIGATE EDIT BREAKPOINTS RUN function [xval, yval] euler (f,a,b,](http://img.homeworklib.com/images/e6ec8bad-32fd-4645-ba8b-202ae5a87c42.png?x-oss-process=image/resize,w_560)
Project 1 PDF-Summer 2019-x A 2019 La HD 16 aälall JW) x MATLAB Functions nt id 1160071 18course id 29592 1 EDE Consider the following two initial value problems along with their exact solutions FILE dy 50e-10z dr 2y, y(0) 40, re [0,2 185 -2 25 -10 y= 4 e 4 and dy cos(T) 2y, y(0) = 2, re [0,6 (6+2m2)e- y= - 2r +T sin( Tx ) +2 cos (Tz) 10 4+2 11 - 1. For each I.V.P. you should write a MATLAB script file to solve the problem ing Euler's method with the following four values of h: h 0.1, 0.01, 0.001, 0.00001 us- 2. Your code should generate a single plot of the four approximate solution curves, the exact solution and the direction field. Be sure to label the axes, the legend and the title to exactly match the information relating to each problem. a table of values including columns for r, ya, yexact corresponding only to h 0.1. The columns must be 3. In addition, please create and the absolute error labeled. printout of your code, both graphs and both tables. You will submit a *It might be easiest to embed everything into a word document for submission
Jsersleskandara\Desktop\New folder (7leuler.m* PUBLI.. VIEW 2 VIGATE EDIT BREAKPOINTS RUN function [xval, yval] euler (f,a,b, y0, h) = floor (b-a) /h +1; snumber of mesh points = (N, 1) creating an empty vector zeros (N, 1); another empty vector xval = zeros yval xval (1) = a: yval (1) y0; Efor i-2:N a+ (i-1) *h; % mesh points xval (i) (i-1) +h*f (xval (i-1), yval (i-1)) yval (i) yval sapproximate end Col 4 Ln 11 euler 14
Homework Answers
%%Matlab code for slope field of ode
clear all
close all
%function 1 for ode
f=@(x,y) 50*exp(-10*x)-2*y;
%Direction field
x=0:0.25:2; y=0:5:40;
[X,Y]=meshgrid(x,y);
dX=ones(size(X));
dY=50*exp(-10*X)-2*Y;
figure(1)
quiver(X,Y,dX,dY)
axis tight
hold on
xx=linspace(0,2,100);
%function for exact solution
y_ext=@(x) (185/4)*exp(-2*x)-(25/4)*exp(-10*x);
yy_ext=y_ext(xx);
figure(1)
plot(xx,yy_ext,'ko-','linewidth',2);
hold on
fprintf('\n\nEuler solution for 1st function\n')
fprintf('\th\txn\tyn\ty_ext\n\n')
hh=[0.1 0.01 0.001 0.00001];
for j=1:length(hh)
h=hh(j);
[x_elr,y_elr1]=euler(f,[0 2],40,h);
plot(x_elr,y_elr1,'r','linewidth',2);
fprintf('\t%.5f \t%.4f \t%f
\t%f\n',h,x_elr(end),y_elr1(end),y_ext(x_elr(end)))
end
legend('Slope field','Exact Sltn','Approx.
Sltn','location','northeast')
title('Euler method solution for 1st function')
%function 2 for ode
f=@(x,y) cos(pi*x)-2*y;
%Direction field
x=0:0.25:6; y=0:.5:3;
[X,Y]=meshgrid(x,y);
dX=ones(size(X));
dY=cos(pi*X)-2*Y;
figure(2)
quiver(X,Y,dX,dY)
axis tight
hold on
%question b.
xx=linspace(0,6,100);
%function for exact solution
y_ext=@(x)
((6+2*pi^2)*exp(-2*x)+pi*sin(pi*x)+2*cos(pi*x))/(4+pi^2);
yy_ext=y_ext(xx);
figure(2)
plot(xx,yy_ext,'ko-','linewidth',2);
hold on
fprintf('\n\nEuler solution for 2nd function\n')
fprintf('\th\txn\tyn\ty_ext\n\n')
hh=[0.1 0.01 0.001 0.00001];
for j=1:length(hh)
h=hh(j);
[x_elr,y_elr1]=euler(f,[0 6],2,h);
plot(x_elr,y_elr1,'r','linewidth',2);
fprintf('\t%.5f \t%.4f \t%f
\t%f\n',h,x_elr(end),y_elr1(end),y_ext(x_elr(end)))
end
legend('Slope field','Exact Sltn','Approx.
Sltn','location','northeast')
title('Euler method solution for 2nd function')
%Function for Euler ode solution
%Euler method
function [x,y]=euler(f,xx,y_in,h)
%function (i)
%f=@(x,y) 50*exp(-10*x)-2*y;
%initial and final x
%x_in=0; x_end=2;
%y_in=40;
x_in=xx(1); x_end=xx(2);
%initial conditions
x(1)=x_in;
y(1)=y_in;
x_max=x_end;
%Final x
N=(x_max-x_in)/h; %number of steps
%Euler iterations
for i=1:N
x(i+1)=x_in+i*h;
y(i+1)=double(y(i)+h*(f(x(i),y(i))));
end
end
%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%
Add Answer to:
the code in the photo for this I.V.P dy/dx= x+y. y(0)=1 i need the two in the photo thank you New folder Bookmark...
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Matlab & Differential Equations Help Needed I need help with this Matlab project for differential equations. I've got 0 experience with Matlab other than a much easier project I did in another...
Matlab & Differential Equations Help Needed
I need help with this Matlab project for differential equations.
I've got 0 experience with Matlab other than a much easier project
I did in another class a few semesters ago. All we've been given is
this piece of paper and some sample code. I don't even know how to
begin to approach this. I don't know how to use Matlab at all and I
barely can do this material.
Here's the handout:
Here's...
3. Consider the differential equation dy 2x2y dx 0, y 1 In the following questions work to 4 decimal places with the initial conditions x = throughout and give your answer to 3 decimal places, or use exact fractions (a) Use the Euler method to calculate an estimate of the value of y after four steps of length h 0.5 [4 marks] (b) Use the Modified Euler method to calculate an estimate of the value of y after two steps...
4. * Using your calculations from 3., plot the exact solution to dy = 1-y, dt y(0) = 1/2, for 0 <ts1, along with the numerical solution given by Euler's method and the trapezoid method, both with stepsize h = 0.1. Give the approximation of y(t = 1) for each numerical method. To distinguish your solutions: (i) Plot the Euler solution using crosses; do not join them with line segments. (ii) Plot the trapezoid solution using squares; again do not...
For the following differential equation: (x^3)dy/dx+y^4+3=0 where dy/dx is the first derivative of y with respect to x, () means power. The equation has initial values y=2.00 at x=1.00 Using Euler method with a step in the x direction of h=0.30: Show the equation to use to generate values of (2 marks) Calculate the missing values of y in the table below I .1.30 1.00 2.00 1.60 For (2 marks)
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Matlab & Differential Equations Help Needed
I need help with this Matlab project for differential equations.
I've got 0 experience with Matlab other than a much easier project
I did in another class a few semesters ago. All we've been given is
this piece of paper and some sample code. I don't even know how to
begin to approach this. I don't know how to use Matlab at all and I
barely can do this material.
Here's the handout:
Here's...
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