matlab代码实现梯形公式逐步减半算法
时间: 2023-06-09 21:03:24 浏览: 44
好的,以下是Matlab代码实现梯形公式逐步减半算法的示例:
```matlab
function [T, h] = TrapezoidRule(f, a, b, TOL)
% Input:
% f: function handle to the function to be integrated
% a: lower bound of integration
% b: upper bound of integration
% TOL: tolerance of error
% Output:
% T: approximation of the integral
% h: step size used in the approximation
% set initial step size
h = (b - a);
% initialize T using the trapezoid rule with the initial step size
T = (h / 2) * (f(a) + f(b));
% loop until the desired tolerance is reached
while true
% update the step size by halving it
h = h / 2;
% compute the new approximation using the trapezoid rule with the
% updated step size
T_new = (h / 2) * (f(a) + 2 * sum(f(a + h:h:b-h)) + f(b));
% check if the absolute error between the new and old approximations
% is less than the desired tolerance
if abs(T_new - T) < TOL
% if the error is less than the tolerance, return the new
% approximation and the step size used
T = T_new;
return;
else
% if the error is not less than the tolerance, update the
% approximation and continue the loop with the new step size
T = T_new;
end
end
end
```
请注意,此函数使用梯形规则的连续逐步减半方法来计算积分,并返回近似积分和使用的步长。调用此函数的示例代码如下所示:
```matlab
% define the function to be integrated
f = @(x) exp(x) / (1 + x);
% set the lower and upper bounds of integration
a = 0;
b = 1;
% set the desired tolerance of error
TOL = 1e-6;
% calculate the approximation of the integral and the step size used
[T, h] = TrapezoidRule(f, a, b, TOL);
% display the results
fprintf('Approximation of the integral: %f\n', T);
fprintf('Step size used: %f\n', h);
```
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