使用Matlab/Maple查找非线性方程的根

问题描述

我很难找到非线性方程的根.我已经尝试过Matlab和Maple两者，并且都给了我相同的错误，即

I am having difficulty in finding roots of a nonlinear equation. I have tried Matlab and Maple both, and both give me the same error which is

Error, (in RootFinding:-NextZero) can only handle isolated zeros

等式如下

-100 + 0.1335600000e-5*H + (1/20)*H*arcsinh(2003.40/H)

等式中的变量为H.

如何找到该方程式的根(或近似根)?

How do I find the roots (or the approximate roots) of this equation?

Matlab代码:功能文件:

Matlab Code:The function file:

function hor_force = horizontal(XY, XZ, Lo, EAo, qc, VA)
syms H
equation = (-1*ZZ) + (H/qc)*(cosh((qc/H)*(XZ- XB))) - H/qc + ZB;
hor_force = `solve(equation);`

主文件:

EAo = 7.5*10^7;
Lo = 100.17;
VA = 2002;

XY = 0;
ZY = 0;

XB = 50;
ZB = -2;

XZ = 100;
ZZ = 0;

ql = 40;

Matlab显示的错误:

Error which Matlab shows:

Error using sym/solve (line 22)
Error using maplemex
Error, (in RootFinding:-NextZero) can only handle isolated zeros

Error in horizontal (line 8)
hor_force = solve(equation);
Error in main (line 34)
h = horizontal(XY, XZ, Lo, EAo, ql, VA)

http://postimg.org/image/gm93z3b7z/

推荐答案

您不需要使用符号工具箱:

You don't need the symbolic toolbox for this:

首先，创建一个匿名函数，该函数可以在输入处使用向量(使用.*和./:

First, create an anonymous function that can take vectors at input (use .* and ./:

equation = @(H) ((-1*ZZ) + (H./qc).*(cosh((qc./H).*(XZ- XB))) - H./qc + ZB);

第二步，创建一个向量，然后将其插入方程式中，以大致找到函数的符号何时变化.最后，使用 fzero 和x0作为第二个输入参数.

Second, create a vector that you afterwards insert into the equation to find approximately when the sign of the function changes. In the end, use fzero with x0 as the second input parameter.

H = linspace(1,1e6,1e4);
x0 = H(find(diff(sign(equation(H)))));  %// Approximation of when the line crosses zero
x = fzero(equation, x0)  %// Use fzero to find the crossing point, using the initial guess x0
x =
   2.5013e+04
equation(x)
ans =
     0

要验证:

您可能想查看此问题有关如何查找非多项式根的更多信息.

You might want to check out this question for more information about how to find roots of non-polynomials.

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