伪谱凸优化的定义域转换

function ydiff = odeExample(t, y, a, b, c)
% Define the differential equation
ydiff = [y(2); a*y(2) - b*y(1) - c*y(1)^3];
end

function [x,y] = pseudoSpectralMethod(a,b,c,x0)
N = 64; % Number of collocation points
x = linspace(-1,1,N)'; % Chebyshev collocation nodes
x = (x+1)*(b-a)/2 + a; % Change the interval to [a,b]

% Define the function handle for the differential equation
f = @(t, y) odeExample(t, y, a, b, c);

% Define the boundary conditions
bc1 = x(1) - x0; % y(a) = x0
bc2 = f(0, [1 0]); % y'(0) = f([1 0])

% Formulate the optimization problem
prob = bvpInit(f, bc1, bc2, x, 'Chebyshev', N-1);

% Solve the optimization problem using bvpSolve
soln = bvpSolve(prob);

% Evaluate the solution at the collocation points
y = soln.y(:,1);

% Plot the solution
figure;
plot(x, y, 'o-');
title('Pseudospectral solution of ODE');
xlabel('x');
ylabel('y');
end