How can I resolve the "Unable to solve collocation" error in MATLAB when trying to solve a nonlinear differential equation with nonlinear boundary conditions?

Question

MOSLI KARIM 2023-12-24

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2063677-how-can-i-resolve-the-unable-to-solve-collocation-error-in-matlab-when-trying-to-solve-a-nonlinea

评论： Torsten 2024-1-3

MIT6()
Pi = 1×251
                   0   0.010000000000000   0.020000000000000   0.030000000000000   0.040000000000000   0.050000000000000   0.060000000000000   0.070000000000000   0.080000000000000   0.090000000000000   0.100000000000000   0.110000000000000   0.120000000000000   0.130000000000000   0.140000000000000   0.150000000000000   0.160000000000000   0.170000000000000   0.180000000000000   0.190000000000000   0.200000000000000   0.210000000000000   0.220000000000000   0.230000000000000   0.240000000000000   0.250000000000000   0.260000000000000   0.270000000000000   0.280000000000000   0.290000000000000
Error using bvp4c
Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in solution>MIT6 (line 26)
    sol=bvp4c(@BVP_ODE,@BC,solinit)%options );
%% 
function  MIT6
clc
close all
format long
global A B eta
A =10 ;  % INTERNAL RADIUS 
B=200;   %% EXTERNEL RADIUS 
eta = B / A;  % THICKNESS RATIO
Mesh=100  ;       %% MESHING 
Pi = 0:0.01:2.5          %%  APPLIED INNER PRESSURE 
R = linspace(A, B, Mesh);
Lambda_theta = zeros(length(Pi), 1);
r_at_A = zeros(length(Pi), length(R));  %%% Specifying the size of matrix containing internal radius
for ik = 1:length(Pi)
    
    %options = bvpset('stats', 'on', 'NMax', 50000);
    solinit=bvpinit(R ,@Guess);
    sol=bvp4c(@BVP_ODE,@BC,solinit)%options );
    zz = deval(sol,R );
    r_at_A(ik,:) = zz(1,:);
    Lambda_theta(ik) = zz(1, 1) / A;
    display(r_at_A)
    figure(1)
    hold on
    plot(sol.x,sol.y(1,:),'LineWidth',3)
    
end
%%%%%%  deformed inner radius at A
a_at_A = (r_at_A(:,1))/A;
%% GRAPHICAL PART  %%%%% 
figure(2)
hold on
set(gca,'FontSize',16)
plot(a_at_A,Pi,'lineWidth',3)
set(get(gca,'Ylabel'),'Rotation',0)
ylabel('$P$','Interpreter','LaTeX','FontSize',20, 'FontWeight', 'normal', 'FontName', 'Times');
%         xlabel('$\Lambda_a ','Interpreter','LaTeX','FontSize',20, 'FontWeight', 'normal', 'FontName', 'Times');
xlabel('$\lambda_a$', 'Interpreter', 'latex', 'FontSize', 20, 'FontWeight', 'normal', 'FontName', 'Times');
grid on
hLegend=legend(['\eta =', num2str(eta)],'Location','SE')
% legend('boxoff')
% legend('Orientation','vertical')
set(hLegend, 'FontSize',18, 'Position', [0.7, 0.8, 0.1, 0.1]);
% Définir une boîte autour du graphe
ax = gca; % Récupérer l'objet axes actuel
set(ax, 'Box', 'on'); % Activer la boîte autour du graphe
%         title('$\alpha = 5$', 'FontSize', 16, 'FontWeight', 'bold', 'Color', 'black', 'Interpreter', 'latex');
%         %%
%          % Add annotations
%          [~, maxIndex] = max(Pi);
%          text(a_at_A(maxIndex), Pi(maxIndex), 'Maximum', 'VerticalAlignment', 'bottom', 'HorizontalAlignment', 'right');
%          xlabel('a/A');
%          ylabel('Pi');
%          title('Pi vs. a/A');
%         
%         
%%        
%         Ajouter la boîte de texte
annotation('textbox', [0.2, 0.6, 0.1, 0.1], 'String', ['Pmax : ', num2str(Pmax)],...
    'FitBoxToText', 'on', 'BackgroundColor','white', 'EdgeColor', 'black','Interpreter', 'latex');
%%
%         % save('pqfile.txt', 'a_at_A', '-ascii');
% Save Lambda_theta to a file (Excel format)
excelFileName = 'Lambda_theta.xlsx';                                
Lambda_theta_cell = num2cell(Lambda_theta);                                        
%xlswrite(excelFileName, Lambda_theta_cell);
%%    % STTING  THE SYSYETME OF ODE
    function dxdy = BVP_ODE(R, y)
        dxdy = [y(2);
            (2/3)*y(2)/R-(2/3)*(y(2)^4/y(1)^3)*R^2];
    end
%%
% SETING THE BOUNDARY CONDITION
    function res = BC(ya, yb)
        
        res = [1 - A^2 / (ya(1)^2 * ya(2)^3) + Pi(ik);
            1 - B^2 / (yb(1)^2 * yb(2)^3)];
    end
    function U = Guess(R)
        U = [  1  % Radial displacement profile
            1];                                       % Initial guess for the second variable
        
        % Initial guess for the second variable
    end
end 

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MOSLI KARIM 2024-1-3

编辑：Torsten 2024-1-3

在 MATLAB Online 中打开

MIT6()

%%

function MIT6

clc

close all

format long

global A B eta

A =10 ; % INTERNAL RADIUS

B=200; %% EXTERNEL RADIUS

eta = B / A; % THICKNESS RATIO

Mesh=100 ; %% MESHING

Pmin =0;

Pmax=2.5;

N =100;

%h = (Pmax - Pmin) /N;

Pi = 0:2.5; %% APPLIED INNER PRESSURE

% Pi=linspace(0,2.51,20 )

R = linspace(A, B, Mesh);

Lambda_theta = zeros(length(Pi), 1);

r_at_A = zeros(length(Pi), length(R)); %%% Specifying the size of matrix containing internal radius

for ik = 1:length(Pi)

%options = bvpset('stats', 'on', 'NMax', 50000);

solinit=bvpinit(R ,@Guess);

sol=bvp4c(@BVP_ODE,@BC,solinit);%options );

zz = deval(sol,R );

r_at_A(ik,:) = zz(1,:);

Lambda_theta(ik) = zz(1, 1) / A;

%display(r_at_A)

figure(1)

hold on

plot(sol.x,sol.y(1,:),'LineWidth',3)

figure(2)

Ur=sol.y(1,:)-sol.x;

figure(2)

hold on

plot(sol.x,Ur)

end

%%%%%% deformed inner radius at A

a_at_A = (r_at_A(:,1))/A;

%% GRAPHICAL PART %%%%%

figure(3)

hold on

set(gca,'FontSize',16)

plot(a_at_A,Pi,'lineWidth',3)

set(get(gca,'Ylabel'),'Rotation',0)

ylabel('$P$','Interpreter','LaTeX','FontSize',20, 'FontWeight', 'normal', 'FontName', 'Times');

% xlabel('$\Lambda_a ','Interpreter','LaTeX','FontSize',20, 'FontWeight', 'normal', 'FontName', 'Times');

xlabel('$\lambda_a$', 'Interpreter', 'latex', 'FontSize', 20, 'FontWeight', 'normal', 'FontName', 'Times');

grid on

hLegend=legend(['\eta =', num2str(eta)],'Location','SE');

% legend('boxoff')

% legend('Orientation','vertical')

set(hLegend, 'FontSize',18, 'Position', [0.7, 0.8, 0.1, 0.1]);

% Définir une boîte autour du graphe

ax = gca; % Récupérer l'objet axes actuel

set(ax, 'Box', 'on'); % Activer la boîte autour du graphe

% title('$\alpha = 5$', 'FontSize', 16, 'FontWeight', 'bold', 'Color', 'black', 'Interpreter', 'latex');

% %%

% % Add annotations

% [~, maxIndex] = max(Pi);

% text(a_at_A(maxIndex), Pi(maxIndex), 'Maximum', 'VerticalAlignment', 'bottom', 'HorizontalAlignment', 'right');

% xlabel('a/A');

% ylabel('Pi');

% title('Pi vs. a/A');

%

%%

% Ajouter la boîte de texte

annotation('textbox', [0.2, 0.6, 0.1, 0.1], 'String', ['Pmax : ', num2str(Pmax)],...

'FitBoxToText', 'on', 'BackgroundColor','white', 'EdgeColor', 'black','Interpreter', 'latex');

%%

% % save('pqfile.txt', 'a_at_A', '-ascii');

% Save Lambda_theta to a file (Excel format)

%excelFileName = 'Lambda_theta.xlsx';

%Lambda_theta_cell = num2cell(Lambda_theta);

%xlswrite(excelFileName, Lambda_theta_cell);

%% % STTING THE SYSYETME OF ODE

function dxdy = BVP_ODE(R, y)

dxdy = [y(2);

(2/3)*y(2)/R-(2/3)*(y(2)^4/y(1)^3)*R^2];

end

%%

% SETING THE BOUNDARY CONDITION

function res = BC(ya, yb)

res = [1 - A^2 / (ya(1)^2 * ya(2)^3) + Pi(ik);

1 - B^2 / (yb(1)^2 * yb(2)^3)];

end

function U = Guess(R)

U = [ R ; % Radial displacement profile

1]; % Initial guess for the second variable

end

This MATLAB code describes the inflation phenomenon of a hollow sphere with an inner radius A and an outer

radius B, composed of a compressible hyperelastic material of Blatz-Ko type. My issue lies in the fact that the pressure curve as a function of the deformed inner radius does not decrease once it reaches its maximum value."

MOSLI KARIM 2024-1-3

BOUNDARY CONDITION AT POINT R.pdf

this my equation sir

Torsten 2024-1-3

My issue lies in the fact that the pressure curve as a function of the deformed inner radius does not decrease once it reaches its maximum value.

Looking at your solution curves, I don't know what you mean (see above).

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How can I resolve the "Unable to solve collocation" error in MATLAB when trying to solve a nonlinear differential equation with nonlinear boundary conditions?

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How can I resolve the "Unable to solve collocation" error in MATLAB when trying to solve a nonlinear differential equation with nonlinear boundary conditions?

7 个评论 显示 5更早的评论隐藏 5更早的评论

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另请参阅

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7 个评论
显示 5更早的评论隐藏 5更早的评论