Solving a differential equation using ode45
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B1, B2, and B3 are 4-D double, and intial condition are phi = 0 at s = 0, d(phi)/ds = 0 at s = 0. I am trying to solve this equation using ode45. EQUATION IS B1*phi + B2*(d(phi)/ds) - B3*(d^2(phi)/ds^2) = 0.
my code
% Define the linear coefficient matrices B at the specific s value
for i = 1:n_node
B(:,:,:,i) = coefficient_linear(nmp_order, GPr, GPt, GPWr, GPWt, NGPr, NGPt, s(i));
end
% Initialize variables
B1 = B(1,:,:,:); % Coefficient B1
B2 = B(2,:,:,:); % Coefficient B2
B3 = B(3,:,:,:); % Coefficient B3
% Define the anonymous function for the equation
equation = @(s, phi_dphi) [phi_dphi(2); -B1.*phi_dphi(1) + B2.*phi_dphi(2) - B3.*(phi_dphi(2).^2)];
% Define the initial conditions
phi0 = 0; % Initial condition for phi
dphi_ds0 = 0; % Initial condition for d(phi)/ds
% Set the options for ode45 (optional)
options = odeset('RelTol', 1e-6, 'AbsTol', 1e-6);
% Solve the equation using ode45
[t, phi_dphi] = ode45(equation, [S_0, S_L], [phi0; dphi_ds0], options); % error at this line of code
% Extract the solution for phi and d(phi)/ds
phi = phi_dphi(:, 1);
dphi_ds = phi_dphi(:, 2);
% Display the results
disp('Solution:')
disp('---------')
disp('s phi d(phi)/ds')
disp([t, phi, dphi_ds]);
I have bold the line of code and the error is
Error using vertcat
Dimensions of arrays being concatenated are not consistent.
댓글 수: 2
KSSV
2023년 5월 25일
Check the dimensions of :
[S_0, S_L]
[phi0; dphi_ds0]
GOBIND KUMAR
2023년 5월 25일
답변 (1개)
The code for the ode45 part can run. No issue with that.
So, I think the problem lies in the computation of the 
. Try fixing that.
. Try fixing that.S_0 = 0;
S_L = 20;
% Initialize variables
B1 = 1; % Coefficient B1
B2 = -2; % Coefficient B2
B3 = 0; % Coefficient B3
% Define the anonymous function for the equation
equation = @(s, phi_dphi) [phi_dphi(2); -B1.*phi_dphi(1) + B2.*phi_dphi(2) - B3.*(phi_dphi(2).^2)];
% Define the initial conditions
phi0 = 1; % Initial condition for phi
dphi_ds0 = 0; % Initial condition for d(phi)/ds
% Set the options for ode45 (optional)
options = odeset('RelTol', 1e-6, 'AbsTol', 1e-6);
% Solve the equation using ode45
[t, phi_dphi] = ode45(equation, [S_0, S_L], [phi0; dphi_ds0], options); % error at this line of code
% Extract the solution for phi and d(phi)/ds
phi = phi_dphi(:, 1);
dphi_ds = phi_dphi(:, 2);
% Test plot
plot(t, phi), grid on
% Display the results
disp('Solution:')
disp('---------')
disp('s phi d(phi)/ds')
disp([t, phi, dphi_ds]);
댓글 수: 4
GOBIND KUMAR
2023년 5월 25일
Sam Chak
2023년 5월 25일
Thanks for your clarification. How do you interpret this ODE?
equation = @(s, phi_dphi) [phi_dphi(2); -B1.*phi_dphi(1) + B2.*phi_dphi(2) - B3.*(phi_dphi(2).^2)];
Does it look this?
How exactly do you perform the 4-D matrix multiplication? If you can show us the math, it will help to resolve the issue.
GOBIND KUMAR
2023년 5월 25일
sir, I am not sure about the multiplication part using B1,B2,B3.
Sam Chak
2023년 5월 25일
I'm not too familiar with some of your math notations. But I think in vector field form, the ODEs should be expressed as follows:
If that is true, then your original ode45 code above was incorrect.
If you are unsure about the matrix multiplication B1, B2, B3, perhaps you can plot out B1, B2, B3. You need to at least provide info about the B's. The ode45 part does not look like a problem yet.
카테고리
도움말 센터 및 File Exchange에서 Ordinary Differential Equations에 대해 자세히 알아보기
2023년 5월 25일
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