Solve multiple eigenvalue ODE problem with bvp4c

Question

Anshuman Pal 2021-9-2

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1445459-solve-multiple-eigenvalue-ode-problem-with-bvp4c

回答： darova 2021-9-5

Hello,

I am following the bvp4c manual to solve an eigenvalue problem with two eigenvalues. I am getting an error `Error using vertcat: Dimensions of arrays being catenated are not consistent`. However, I think that this error might be due to some other inconsistency in my code. Could someone please help?

My code:

clear all
% parameters
global L Num
Num = 3000;  % number of grid points. 3000 is plenty.
L = 1.0 ; % length of buckled portion of rod 
tau0_init = 0;      % 2 eigenvalues
deltaL_init = 0.1*L;
ss = linspace(0, L, Num);
solinit = bvpinit(ss, @mat4init, [tau0_init, deltaL_init]);
options = bvpset('Stats','on','RelTol',1e-5,'NMax',Num);
sol = bvp4c(@bvp_RHS, @bvp_BC, solinit, options);
fprintf('The eigenvalues are approximately %.2f.\n',sol.parameters)
figure
plot(sol.x, sol.y)
xlabel('s')
grid
legend(compose('$y_{%2d}$',1:11), 'Location','bestoutside', 'Interpreter','latex')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function yinit = mat4init(x)
% initial guess for the solution
global L
yinit = [-sin(pi/L*x)     % theta
         -pi/L * cos(pi/L*x)  % theta'
         0.1               % x
         0.1                % y   
    ];
end
function dyds = bvp_RHS(x, y, tau0, deltaL)
% Total 4 variables.
% NB: eigenvalues tau0 and deltaL must be a function input even though if not present 
% in any equation below.
global L 
dyds = [ y(2)                     
         -tau0*sin(y(1)) +(L-x)*cos(y(1))    
         cos(y(1))                   
         sin(y(1))                   
        ];
end
function res = bvp_BC(yL, yR, tau0, deltaL)
% BCs at L and R boundaries, with constraint for eigenvalues tau0 and deltaL.
global L 
res = [ yL(1)
        yL(2)
        yL(3)
        yL(4)
        yR(1)
        yR(3)- 0.5*(L-deltaL)
        ];
end