Solving non linear equation with a range in MATLAB (problem)

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Abdullah Nasir 2018-2-7

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评论： JK 2018-2-7

I need to solve below non-linear equation with a range but cannot find a way to do it

Range of (x) is -40 to 30 with increments of 5. (x) is known but I need to find range of (y) and plot (x) vs (y). Please with the answer provide an explanation also. Thank you

p=0.5

S=(sin(y-x)-p*sin(x)*sin(y))=0

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Answer 1

JK 2018-2-7

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在 MATLAB Online 中打开

Hi Abdullah,

here is the code with comments:

x=[-40:5:30]';      % x in rad or °? Matlab uses rad
n = size(x,1);      % numbers of calculations
yy=zeros(n,1);      % preallocation of yy to make it a column-vector 
for i=1:n
  yy(i)=fsolve(@(y) fun(x(i),y),0); % solve implicit equation
end
figure
plot(x,yy)          % plot it
function S=fun(x,y)
    S=(sin(y-x)-0.5*sin(x)*sin(y)); % your function
end

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Walter Roberson 2018-2-7

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

JK 2018-2-7

yy(i)=fsolve(@(y) fun(x(i),y),0);

yy(i) is y(x(i))
fsolve is the solver for implicit equations, it solves f(x)=0 for x. You can also use fzero is this case which is probably faster.
@(y) fun(x(i),y) is an anonymus function. I uses the x(i) value by the time it is called and solves the function fun(x,y) for y.
0 is the initial guess for y. For a simple equation, 0 will normally suffice as a starting point. If the equation gets more complicated try better starting values.

for using ° instead of rad try

x=[-40:5:30]'/180*pi;

...

plot(x/pi*180,yy/pi*180)

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Answer 2

Walter Roberson 2018-2-7

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在 MATLAB Online 中打开

syms x y
p = 0.5;
eq = (sind(y-x)-p*sind(x)*sind(y)) == 0;
Y = simplify(solve(eq, x));

This gives you an explicit formula for Y. You can substitute particular numeric values for x into the formula.

MATLAB will return two expressions. If you analyze the expressions, they turn out to differ by 180 degrees. Further analysis shows that there an an infinite number of other solutions that are 180 apart.

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Walter Roberson 2018-2-7

在 MATLAB Online 中打开

Do not assign numeric values to x before the code that follows.

xvec = -40:5:30;
syms x y
p = 0.5;
eq = (sind(y-x)-p*sind(x)*sind(y)) == 0;
Y = simplify(solve(eq, y));         %typo fixed on this line
Yn = double( subs(Y, x, xvec) );
plot(xvec, real(Yn));