MATLAB: How to solve transcendental equations in matlab

computationalmathematicsmatlab functionmatrix manipulationphysicstranscendental equations

I am practicing solving transcendental equations in matlab I have the given equation and I want to solve for x

tan(((0.9)*pi/w)*sqrt(1.468^2-x.^2))- sqrt((x.^2-1.458^2))/(sqrt(1.468^2-x.^2))==0

plotting w varies from 1.55 to 5 I tried all day but I cannot find solution, I tried with fzero(fun,xo) without success any suggestion?

Best Answer

This is a complex-valued function. Just from visual inspection, it is apparent that the real part of this function has infinitely many solutions. The imaginary part, however, appears to have a finite number of zeros. Are those the solutions you are looking for?

x=linspace(-2*pi,2*pi,1E4);
w=1.55;
f=tan(((0.9)*pi/w)*sqrt(1.468^2-x.^2)) - sqrt((x.^2-1.458^2))./(sqrt(1.468^2-x.^2));
figure('color','w')
plot(x,real(f))
hold on
plot(x,imag(f))
set(gca,'YLim',[-10 10])

Related Solutions

MATLAB: How to get phase section of this equation

Try this


W = 0.1:0.1:1.5;
odefun = @(t,X,w) [X(2); -0.05*X(2)-sin(X(1))+0.7*cos(w*t)];
t = 0:0.1:10;
ic = [0;0];
X_sol = cell(1,numel(W));
for i=1:numel(W)
    [~, X_sol{i}] = ode45(@(t,X) odefun(t, X, W(i)), t, ic);
end
tiledlayout('flow')
for i=1:numel(X_sol)
    nexttile
    plot(X_sol{i}(:,1), X_sol{i}(:,2));
    xlabel('x')
    ylabel('y')
    title(['w = ' num2str(W(i))]);
end

The tiledlayout will work for R2019b and onward. For older versions using the following lines to plot the figure

figure;
for i=1:numel(X_sol)
    subplot(4,4,i);
    plot(X_sol{i}(:,1), X_sol{i}(:,2));
    xlabel('x')
    ylabel('y')
    title(['w = ' num2str(W(i))]);
end

MATLAB: I keep getting this error, ” Failure in initial objective function evaluation. FSOLVE cannot continue.”

fsolve fails to continue because the function MyFunction doesnot not have access to the variables (M1, M2, M3...). You can use global variables for MyFunction to work without errors.

global param 
param.M1 = 0.5;
param.M2 = 0.75;
param.M3 = 0.95;
param.M4 = 1.102;
param.M5 = 1.102;
param.K = 1;
param.Kc = 1;
param.Kk = 3;
param.KR = 0.95;
param.G = 0.001; 
param.GR = 0.1;
param.Gc = 0.005;
param.B = 0.15;
param.A= 1;
param.w= 1;
x0 = [1 1 1 1 1];
fun=@MyFunction;
x = fsolve(fun,x0);
function F = MyFunction(x)
    global param 
    F(1 )= x(1).*(-param.M1.*(param.w.^2) + param.K + param.Kc +param.KR + param.G.*1i.*param.w) - (param.A.*(exp(1i.*param.w)) + param.Kc.*x(4) + param.KR.*x(3));
    F(2) = x(2).*(-param.M2.*(param.w.^2) + param.K + param.Kc +param.KR + param.G.*1i.*param.w) - (param.A.*(exp(1i.*param.w)) + param.Kc.*x(5) + param.KR.*x(3));
    F(3) = x(3).*(-param.M3.*(param.w.^2) + 2.*param.Kk + param.GR.*1i.*param.w) - (param.KR.*(x(1) + (x(2))));
    F(4) = x(4).*(-param.M4.*(param.w.^2) + param.Kc + param.Kk + param.Gc.*1i.*param.w) - param.B.*1i.*(param.w.^3).*((x(4)).^3) -param.A.*(exp(1i.*param.w)) - param.Kc.*x(1);
    F(5) = x(5).*(-param.M5.*(param.w.^2) + param.Kc + param.Kk + param.Gc.*1i.*param.w) - param.B.*1i.*(param.w.^3).*((x(4)).^3) - param.A.*(exp(1i.*param.w)) - param.Kc.*x(2);
end

Best Answer

Related Solutions

MATLAB: How to get phase section of this equation

MATLAB: I keep getting this error, ” Failure in initial objective function evaluation. FSOLVE cannot continue.”

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