solve runge kutta method

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Mariam Gasra 2019-5-15

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https://ww2.mathworks.cn/matlabcentral/answers/462345-solve-runge-kutta-method

关闭： MATLAB Answer Bot 2021-8-20

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lamda=0.2;
mu=0.8;
h=0.1;                                             % step size
x = 0:h:5;                                         % Calculates upto y(3)
Y = zeros(1,length(x)); 
y(1) = 0.2; % redo with other choices here. 
    % initial condition
%F_xy = @(??,??) (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;                  
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 = [0,5]; y0 = -0.5;
[tx, yx] = ode45(F_xy, tspan, y0)
plot(x,y,'o-', tx, yx, '--')