Please provide pseudocode and code. *note pseudocode must not have any matlab syntax, only english sentences. I am providing the code below, and the objective according to the homework assignment (also attached) is to improve upon this code and answer questions 1 and 2. CODE:

function y = myeuler(func,yO,tO,tf,N)

h = (tf-tO)/N; %size of timestep

t = tO: h : tf; %array of timesteps

y = zeros(length(yO),N+1); %preallocate y

y(:,1) = yO; %column vector% %set initial condition

for k=1:N

%euler iteration

y(:,k+1)=y(:,k)+h*func(t(k),y(:,k));

end %copy paste this and improve upon it for homework

That is the code^, again the objective is to improve upon it .

Fun with Epidemics Math 3343 Introduction to Mathematical Software Homework5 Due on Monday 02/26/2018 in class. The Computational Tool The Improved Euler Method improves upon the standard euler method by using a trapezoid to approximate the integral , y(t)) dt, rather than a rectangle. The goal is the same: to approximate a solution to the first order initial value problem: dy(t) dt y(to) yo = at N +1 evenly spaced points: to, t1,., tv. The improved Euler Method is described by the iteration The vector yk is meant to approximate y(tk). 1. (20 points) Write a pseudocode for the Improved Euler timestepping method. 2. (40 points) Implement your Improved Euler code as a Matlab function names ieuler.m for solving ordinary differential equations, using the following input and outputs Input The vector-valued function of two variables: f. An initial condition vector yo A starting time to . An ending time tw. . The number of timesteps, N. Output . A matrix y whose columns approximate the solution y(t) for each value to, tht Your code should begin: function y ieuler(func.yo,to, tt, Nt) Fun with Epidemics Math 3343 Introduction to Mathematical Software Homework5 Due on Monday 02/26/2018 in class. The Computational Tool The Improved Euler Method improves upon the standard euler method by using a trapezoid to approximate the integral , y(t)) dt, rather than a rectangle. The goal is the same: to approximate a solution to the first order initial value problem: dy(t) dt y(to) yo = at N +1 evenly spaced points: to, t1,., tv. The improved Euler Method is described by the iteration The vector yk is meant to approximate y(tk). 1. (20 points) Write a pseudocode for the Improved Euler timestepping method. 2. (40 points) Implement your Improved Euler code as a Matlab function names ieuler.m for solving ordinary differential equations, using the following input and outputs Input The vector-valued function of two variables: f. An initial condition vector yo A starting time to . An ending time tw. . The number of timesteps, N. Output . A matrix y whose columns approximate the solution y(t) for each value to, tht Your code should begin: function y ieuler(func.yo,to, tt, Nt)