分享一个打靶法求解两点边值问题的Matlab函数
function varargout = shooting_two_point_boundary(varargin)% ==========================================================
% 函数名：shooting_two_point_boundary.m
% 基于打靶法计算两点边值问题，仅针对二阶微分方程
% author: xianfa110.
% blog： <a href="http://blog.sina.com.cn/xianfa110" target="_blank">http://blog.sina.com.cn/xianfa110</a>
% 函数形式：
% = shooting_two_point_boundary(@fun,,,h);
% 输入：
% fun = 函数名;
% y_0 = 函数初值;
% y_end = 函数终值;
% x_0 = 自变量初值;
% x_end = 自变量终值;
% h = 积分步长;
% 输出：
% result = ;
% err = 误差;
% z0 = y'初值;
% ===========================================================
% 函数fun：4y''+yy' = 2x^3 +16 ; 2<= x <=3
% 写法：
% function f = fun(y,x)
% dy = y(2);
% dz = (2*x^3+16-y(1)*y(2))/4;
% f = ;
% ===========================================================
% 注意:y(1) = y，y(2) = y'。
% ===========================================================
F = varargin{1};
y_0 = varargin{2}(1);
y_end = varargin{2}(2);
x_0 = varargin{3}(1);
x_1 = varargin{3}(2);
ts = varargin{4};
t0 = x_0-0.5;
flg = 0;
kesi = 1e-6;
y0 = rkkt(F,,x_0,x_1,ts);
n = length(y0(:,1));
if abs(y0(n,1)-y_end)<=kesi
flg=1;
else
t1=t0+1;
y1=rkkt(F,,x_0,x_1,ts);
if abs(y1(n,1)-y_end)<=kesi
flg=1;
end
end
if flg ~= 1
while abs(y1(n,1)-y_end) > kesi
% ==========插值法求解非线性方程=============== %
t2 = t1-(y1(n,1)-y_end)*(t1-t0)/(y1(n,1)-y0(n,1));
y2 = rkkt(F,,x_0,x_1,ts);
t0=t1;
t1=t2;
y0=y1;
y1=y2;
end
end
x = x_0:ts:x_1;
out = ;
varargout{1} = out;
varargout{2} = abs(y1(n,1)-y_end);
varargout{3} = t1;
参考文献：数值计算原理
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转自：http://blog.sina.com.cn/s/blog_408540af0100b7mi.html
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