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solve runge kutta for eqution of one variable

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Mariam Gasra
Mariam Gasra on 13 May 2019
lamda=0.2;
mu=0.8;
h=0.5; % step size
x = 0:h:100; % Calculates upto y(3)
Y = zeros(1,length(x));
%y(1) = [-0.5;0.3;0.2];
y(1) = -0.5; % redo with other choices here.
% initial condition
F_xy = @(t,%%) (lamda^2/(lamda+mu)^2)*exp(-2*(lamda+mu)*t)+((2*mu*lamda)/(lamda+mu)^2)*exp(-(mu+lamda)*t)+mu^2/(lamda+mu)^2; % 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
% validate using a decent ODE integrator
tspan = [0,100]; y0 = -0.5;
[tx, yx] = ode45(F_xy, tspan, y0)
plot(x,y,'o-', tx, yx, '--')
how can i correct the function to run the code if i have this equation ?

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