Question

please writed a code using matlab that performs modified eulers method and do the following

2. Use the code to solve the following problem. y = 1+ 15t52. y(1) = 2, Exact Solution y(t) = ?Int + 21. (a) Run the code for N = 10, 20, 100 (b) Compare the approximation values at time t = 2 (both methods) with the exact solution. (c) Graph the two methods and the exact solution in the same graph.

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc
clear all
close all
format long
t=2;
f=@(t,y) 1+y/t;
hold on;
for N=[10,20,100]
[T,Y]=euler_modified(f,1,2,2,N);
fprintf('FOr N=%d, At t=2, Y(2) is %f,error is %.4e\n',N,Y(end),abs(Y(end)-2*log(t)-2*t));
plot(T,Y);
end
legend('N=10','N=20','N=100')
function [T,Y] = euler_modified(f,x0,xn,y0,n)
h=(xn-x0)/n;
T=[];
Y=[];
while x0<=xn
T=[T x0];
Y=[Y y0];
k=y0+h*f(x0,y0);
x1=x0+h;
y1=y0+h/2*(f(x0,y0)+f(x1,k));
x0=x1;
y0=y1;
end
end

MATLAB R2018a Figure 1 X Search Documentation Pradeep EDITOR НOME PLOTS APPS fEile Edit View Insert Tools Desktop Window Help Find Files Insert Comment % 에 Go To FCompare New Open Save Indent Print QFind 5.5 FILE NAVIGATE EDIT C: Windows System32 N 10 N-20 E x Current Folder X 5 N 100 Name 5 X ahk.m X bisectionmethodbypradeep.m m 0409 13 A 4.5 1029 14 1033 15 1036 16 4 1040 17 1045 18- 1046 19 3.5 1049 20 1055 21 3082 3 22 Advancedlnstallers 23 af-ZA 24 am-et 2.5 25 AppLocker 26 appraiser 27 Details A 2 1.1 1.6 1.2 1.3 1.4 1.5 1.7 1.8 1.9 2 Com Workspace New X Name Value FOr N 10, At t=2, Y(2) is 5.017366, error is 3.6893e-01 f N t @(ty)1+y/t FOr N-20, At t=2, Y (2) is 5.201686, error is 1.846le-01 100 FOr N 100, At t-2, Y (2) is 5.349363, error is 3.6931e-02 fx> 2 1x100 doubl 1x1 double T 1x100 double Y euler_modified Ln 27 Col 4 ENG 8:01 AM Type here to search IN 11/26/19

Kindly revert for any queries

Thanks.