Question

Emergency please!!!!

Last two numbers digit: 11

1) (35 pts) In this problem the last two digits of your student number will be important. Let n, be a number equal to the last digit of your student number, na be a number equal to the last two digits of your student number. That is, if the last two digits of your student number is 83 then, n = 3, n2 = 83. Consider the predator-prey equations: dx =ax - bxy dt dy E-cx + dxy dt with initial conditions x 0 =2+ and y 0 =1+ In the equations a, b, c, d are constants and their n2 n values are given by: a =2+ b=a* 0.7+ 100' Using midpoint method and a step size of h = 0.25, solve the predator-prey equations untilt becomes 6. For the solutions you can only use a calculator and you have to show all the details. Submissions involving a solution obtained using a Matlab/Octave script (and/or a function) or any other computer program will not receive any points. After you complete the solution, load your results into Matlab/Octave or MS Excel or a similar spread-sheet program and produce two figures. The first figure should have x vs. t and y vs. t on the same graph and the second figure should contain y vs. x plot.

Answer 1

Hey,

Note: 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

n1=3;

n2=11;

a=2+n2/100;

b=a*(0.7+n1/100);

c=a/4;

d=c/2;

h=0.25;

f=@(t,y) [a*y(1)-b*y(1)*y(2),-c*y(1)+d*y(1)*y(2)];

[T,Y]=runge2(f,[0,6],[2+n1/5,1+n1/10],0.25);

plot(T,Y);

legend('x(t)','y(t)');

figure;

plot(Y(:,1),Y(:,2));

function [t,ystar]=runge2(f,tspan,y0,h)

t=tspan(1):h:tspan(2);

ystar = zeros(length(t),2); % Preallocate array (good coding practice)

ystar(1,:) = y0; % Initial condition gives solution at t=0.

for i=1:(length(t)-1)

k1 = f(t(i),ystar(i,:)); % Approx for y gives approx for deriv

y1 = ystar(i,:)+k1*h/2; % Intermediate value

k2 = f(t(i),y1); % Approx deriv at intermediate value.

ystar(i+1,:) = ystar(i,:) + k2*h; % Approximate solution at next value of y

end

end

10 MATLAB Window Help 53% O Tue 6:51 PM a iii HOME PLOTS APPS tion $ Pradeep MATLAB R2020a - academic use EDITOR PUBLISH VIEW OOO Figure 1 - File Edit View Insert Tools Desktop Window Help Figure 2 Insert Tools Desktop Window Help La Find Files Compare New Open Save Print 29 FILE NA /Users x 1029 14 xit) vt) 12 ya Current Folder Name A Published Support Packages untitled1 10 al.m a2.m 8 Value 2.4500 1.8375 0.6125 0.3063 @(t,y)(a*y(1)-b*y... 0.2500 5 45 1x25 double 25x2 double 6 a3.m a4.m a5.m Xabsolute.m absolute Mat.m add.m 2 0 -2 2 4 6 8 10 12 14 -4 x 100 0 0.5 1 1.5 2 2.5 3 addBoarder.m addemup.m addn.m AdjustValue.m ADquant.m age.m ahk.m an_c2f.m anagram.m APolygon.m area.m areaperin.m arnoldi.m assign.m average.m backsubs.m ballTemp.m Barchart.png BeforePosting.m bin_coeff.m binary2decimal.m binary alao.m Details UTF-8 script / runge2 Ln 55 Col4 JUN 2 tv A W