oderk4.m

4阶龙格库塔方法求常微分方程的数值算法的函数子程序。

function [t,y] = odeRK4(diffeq,tn,h,y0)
% odeRK4  Fourth order Runge-Kutta method for a single, first order ODE
%
% Synopsis:  [t,y] = odeRK4(fun,tn,h,y0)
%
% Input:     diffeq = (string) name of the m-file that evaluates the right
%                     hand side of the ODE written in standard form
%            tn  = stopping value of the independent variable
%            h   = stepsize for advancing the independent variable
%            y0  = initial condition for the dependent variable
%
% Output:    t = vector of independent variable values:  t(j) = (j-1)*h
%            y = vector of numerical solution values at the t(j)

t = (0:h:tn)';                   %  Column vector of elements with spacing h
n = length(t);                   %  Number of elements in the t vector
y = y0*ones(n,1);                %  Preallocate y for speed
h2 = h/2;  h3 = h/3;  h6 = h/6;  %  Avoid repeated evaluation of constants    

%  Begin RK4 integration; j=1 for initial condition
for j=2:n
   k1 = feval(diffeq, t(j-1),    y(j-1)        );
   k2 = feval(diffeq, t(j-1)+h2, y(j-1)+h2*k1  );
   k3 = feval(diffeq, t(j-1)+h2, y(j-1)+h2*k2  );
   k4 = feval(diffeq, t(j-1)+h,  y(j-1)+h*k3   );
   y(j) = y(j-1) + h6*(k1+k4) + h3*(k2+k3);
end