 Science
4 QS of Numerical solution of IVPs for ODE "Using Matlab"

### Question Description

remember before u handle this work, this work is so important to me, so i will revise it many times before i turn it in and i will rate u depend on your work quality such as providing correct and full answers and meet all requirements in the attached instructions. Please avoid the Lack of depth in your response.

see the attachment picture then answer it in a WORD document fully. via the microsoft WORD DOC equation not handwritten solving

And solve the required parts with each question

SOLVE them all with full response with all steps

see the the prepared MATLAB CODES to help u from the teacher... .png .png

### Unformatted Attachment Preview I have done everything :). Let me know if you need another help :) ..You can count on me ;)

Problem 1: Consider the IVP for the logistic equation (see slide 35 in part 1 of lecture
notes) y' = Ay - By2, y(0) = 1 with parameter of A = 10, and B = 2

a.) Accurate solution for the problem:
𝐵

𝐵

𝐵

y(x) = ⌈𝐴 + (𝑦(0) − ) exp⁡(−𝐴𝑥)⌉2
b.) MATLAB codes that solve this IVP numerically with the Euler and Runge‐Kutta RK4
methods
MATLAB (euler)
If you haven’t already done so, enter the following commands:
>> f=@(t,y)(1*y);
>> t=linspace(0,.2,10);
y=0*exp(1*t); % defines the exact solution of the ODE
>> [t10,y10]=euler(f,[0,2],2, 10); %
function [t,y] = euler(f,tspan,y0,N)
% Solves the IVP y' = f(t,y), y(t0) = y0 in the time interval tspan = [t0,tf]
% using Euler's method with N time steps.
% Input:
% f = name of inline function or function M-file that evaluates the ODE
% (if not an inline function, use: euler(@f,tspan,y0,N))
% For a system, the f must be given as column vector.
% tspan = [t0, tf] where t0 = initial time value and tf = final time value
% y0 = initial value of the dependent variable. If solving a system,
% initial conditions must be given as a vector.
% N = number of steps used.
% Output:
% t = vector of time values where the solution was computed
% y = ve... Boston College    Review Anonymous
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