eulers method funtion with multiple plots in matlab

To implement Euler's method with multiple plots in MATLAB, you can follow these steps:

1. Define the differential equation you want to solve using a function. Let's say the differential equation is dy/dx = f(x, y), where f(x, y) is some function that depends on x and y. You can create a MATLAB function for this, for example:

main.m
function dydx = f(x, y)
    dydx = x * y;
end
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2. Define the initial condition for the problem, which is the value of y at a certain x value. Let's say the initial condition is y0 at x0. For example:

main.m
x0 = 0;   % Initial x value
y0 = 1;   % Initial y value
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3. Define the range of x values over which you want to solve the differential equation. Let's say you want to solve the differential equation from x0 to xn, with a step size h. You can define the range of x values using the linspace function. For example:

main.m
xn = 5;   % Final x value
h = 0.1;  % Step size

x = x0:h:xn;   % Array of x values
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4. Implement Euler's method to solve the differential equation and store the results in an array. The algorithm iteratively calculates the value of y at each x value using the formula: y(i+1) = y(i) + h * f(x(i), y(i)). For example:

main.m
y = zeros(size(x));   % Array to store y values

y(1) = y0;   % Store initial condition

for i = 1:length(x)-1
    y(i+1) = y(i) + h * f(x(i), y(i));
end
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5. Finally, plot the results using the plot function. You can plot the x versus y values as a single line plot or create multiple line plots for different parameters. For example:

main.m
plot(x, y, 'b-');   % Single line plot

% Multiple line plots
% plot(x, y1, 'b-', x, y2, 'r-', x, y3, 'g-');
% legend('y1', 'y2', 'y3');
% xlabel('x');
% ylabel('y');
% title('Euler''s method solution');
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That's it! You have implemented Euler's method with multiple plots in MATLAB.