composite simpson's rule的matlab code

以下是使用复合辛普森法计算函数f(x)在区间[a,b]上的定积分的MATLAB代码：

function I = composite_simpsons_rule(f, a, b, n)
% f: 被积函数
% a, b: 积分区间
% n: 将区间[a,b]等分成n个子区间

h = (b-a)/n; % 子区间宽度
x = a:h:b; % 子区间端点

% 计算子区间内的积分
I = f(x(1)) + f(x(end)); % 首尾两点的函数值
for i = 2:n
    if mod(i,2) == 1 % 奇数子区间
        I = I + 4*f(x(i));
    else % 偶数子区间
        I = I + 2*f(x(i));
    end
end

I = I*h/3; % 计算积分值
end

使用示例：

f = @(x) x.^2.*exp(-x); % 定义被积函数
a = 0; b = 2; % 积分区间
n = 10; % 将区间等分成10个子区间
I = composite_simpsons_rule(f, a, b, n); % 计算积分
disp(I); % 显示积分值

相关问题

复合simpson算法设计matlab

复合Simpson算法是一种数值积分方法，用于估计函数在给定区间上的定积分。它是通过将区间分成若干个小区间，然后在每个小区间上应用Simpson公式来计算定积分的近似值。在Matlab中，可以使用以下代码实现复合Simpson算法：

function I = composite_simpson(f, a, b, n)
% f是被积函数，a和b是积分区间的下界和上界，n是区间数
h = (b - a) / n;
x = a:h:b;
y = f(x);
I = h / 3 * (y(1) + 4 * sum(y(2:2:end-1)) + 2 * sum(y(3:2:end-2)) + y(end));
end

其中，f是被积函数，a和b是积分区间的下界和上界，n是区间数。函数返回定积分的近似值。

simpson在matlab

Simpson's rule is a numerical integration method used in Matlab to approximate the definite integral of a function. The general syntax for using Simpson's rule in Matlab is:

integral = integral(@(x) f(x), a, b, 'Method', 'Simpson');

Where `f(x)` is the function to be integrated, `a` and `b` are the lower and upper limits of integration, and `'Method', 'Simpson'` specifies that Simpson's rule should be used.

Alternatively, you can use the `quad` function in Matlab, which automatically selects the appropriate integration method based on the properties of the function being integrated. To use Simpson's rule with `quad`, you can specify the method as follows:

integral = quad(@(x) f(x), a, b, [], [], 'Simpson');

Again, `f(x)` is the function to be integrated, and `a` and `b` are the lower and upper limits of integration. The additional empty brackets `[]` specify that the default tolerance and maximum number of function evaluations should be used.