4th order Runge-Kutta Problem in Special ranges

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Rooter Boy
Rooter Boy 2021-1-18
评论： Rooter Boy 2021-1-18
I want to solve this question below in Matlab but i didn't do it. This is simple question but i can't do it. If someone will help me, i will be very happy.
Question: Write a Matlab code that finds the approximate solution of the initial-value problem y '= - 2x-y, y (0) = - 1 using the 4th order Runge-Kutta method for the h = 0.1 step interval in the range [0.0,0.6].
Note: The 4th Order Runge-Kutta method is expressed as follows;
..................................................................................................................................................
Original Question:
I tried this code block, but it didn't work:
clc; % Clears the screen
clear all;
h=0.1; % step size
x = 0:h:3; % Calculates upto y(3)
y = zeros(1,length(x));
%y(0) = [0.0;0.6]
y(0) = -1; % redo with other choices here. % initial condition
F_xy = @(x,y) -2*x-y; % change the function as you desire
for i=1:(length(x)-1) % calculation loop
k_1 = F_xy(x(i),y(i));
k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);
k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));
k_4 = F_xy((x(i)+h),(y(i)+k_3*h));
y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; % main equation
end

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回答（1 个）

Alan Stevens
Alan Stevens 2021-1-18
Change
y(0) = -1;
to
y(1) = -1;
Matlab indices start at 1 not zero.
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James Tursa
James Tursa 2021-1-18
So when I make these changes
h=0.1;
x = 0:h:0.6;
y(1) = 0.2;
F_xy = @(x,y) y-y^2;
and run your code I get the following:
>> y(2)
ans =
0.2165
So, again, it looks like things are working to me.
Rooter Boy
Rooter Boy 2021-1-18
Sir, thank you so much. The answer is probably like you said.

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