Solving system of ODEs using Euler's method and 4 th order Runge Kutta method.

Hi, im going to ask how to solve this problem?

Using time step, ℎ = 0.2, solve the model using Euler method and 4 th order Runge Kutta method. Plot the solutions

[tirah azman]

f=@(t,y) [(20*(-y(1) + Heaviside(y(1)-a) -y(2))) ; (y(1) - 0.15*y(2))];
y=[0.25;0];
h=0.2;
t=0;
a=0.2;
for i=1:1000
    if y(1)<a
        Heaviside((y(1)-a)) =0;
    else
       Heaviside(y(1)-a) =1;
    end
    plot(t,y(1),'linewidth','b.',t,y(2),'linewidth','r.'); hold on
    s=f(t,y);
    y=y+h*s;
    t=t+h;
end
hold off
title('ERP')
xlabel('Time')
ylabel('mV')

[tirah azman]

the code still warning at heaviside fx

Answer 1

[Gargi Patil]

Hi,

The given code throws the error "Array indices must be positive integers or logical values.". The code in the if-else is written for Heaviside as an array rather than a function making (y(1) - a) an index value. Indices for an array can only be integers while the given index value is a fractional value.

This can be resolved by creating a user-defined function as follows:

function y = Heaviside(x)
    if x < 0
        y = 0;
    else
        y = 1;
    end
end

MATLAB also has a pre-defined function heaviside which can be directly used.

Furthermore, the plot command will also throw an error as the property LineWidth expects positive numerical values. The code can be rectified by removing the property LineWidth or specifying a numeric value for it as follows:

plot(t,y(1),'b.',t,y(2),'r.'); 
%or
plot(t,y(1), 'b.',t,y(2), 'r.', 'LineWidth', 5);

For further information about code for solving ODEs using Runge-Kutta 4th Order Metod and Euler's Method, you can refer to the following resources:

https://in.mathworks.com/matlabcentral/answers/460395-runge-kutta-4th-order-method

https://in.mathworks.com/matlabcentral/fileexchange/29851-runge-kutta-4th-order-ode

https://in.mathworks.com/matlabcentral/answers/278300-matlab-code-help-on-euler-s-method

https://in.mathworks.com/matlabcentral/fileexchange/72522-euler-method