MATLAB数值积分：基于牛顿-柯茨公式的定步长和自适应积分方法

function [ integration ] = CompoInt( func, left, right, step, mode )

% 分段积分牛顿-柯茨公式；

% 输入5个参数：被积函数(FUNCTIONHANDLE)'func'，积分上下界'left'/'right'，步长'step'，

% 模式mode共三种('midpoint','trapezoid','simpson')；

% 返回积分值；

switch mode

% 仅仅是公式不同

case 'midpoint'

node = left; integration = 0;

while (node + step <= right) % 按照给定步长开始分段积分

pieceInt = step*(func(node + step/2)); % 使用中点积分公式

integration = integration + pieceInt; node = node + step;

end

if (node < right) % 补齐最后一段积分

pieceInt = (right - node)*(func((node + right)/2));

integration = integration + pieceInt;

end

case 'trapezoid'

node = left; integration = 0;

while (node + step <= right)

pieceInt = step*(func(node) + func(node + step))/2; % 使用梯形公式

integration = integration + pieceInt; node = node + step;

end

if (node < right)

pieceInt = (right - node)*(func(node) + func(right))/2;

integration = integration + pieceInt;

end

case 'simpson'

node = left; integration = 0;

while (node + step <= right)

pieceInt = step*(func(node) + 4*func(node + step/2) + func(node + step))/6; % 使用辛普森公式

integration = integration + pieceInt; node = node + step;

end

if (node < right)

pieceInt = (right - node)*(func(node) + 4*func((node + right)/2) + func(right))/6;

integration = integration + pieceInt;

end

end