Second order non linear differential

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Alessandro Meda 2024-6-1

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评论： Manikanta Aditya 2024-6-3

I have to solve the following equation: y''(s) + cos(y) = 0

BC: y(0) = pi/2 and y(L/4) = 0

I actually have no idea what function is the correct one in this case or even if MatLab can solve this, do you have any suggestion?

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Torsten 2024-6-2

Use bvp4c:

https://uk.mathworks.com/help/matlab/ref/bvp4c.html

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回答（1 个）

Manikanta Aditya 2024-6-1

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编辑：Manikanta Aditya 2024-6-1

在 MATLAB Online 中打开

Hi @Alessandro Meda

Solving a second-order nonlinear differential equation analytically can be challenging, and often such equations do not have closed-form solutions. However, MATLAB can be used to solve this numerically.

You can use the ode45 function, which is a versatile solver for ordinary differential equations.

https://in.mathworks.com/help/matlab/ref/ode45.html

Check this script which will help you:

function solve_nonlinear_ode
    % Initial conditions
    y0 = [0; 0]; % y(0) = 0, y'(0) = 0
    % Time span
    tspan = [0 10];
    % Solve the system
    [t, y] = ode45(@nonlinear_ode, tspan, y0);
    % Plot the solution
    figure;
    plot(t, y(:,1));
    xlabel('s');
    ylabel('y(s)');
    title('Solution of y''''(s) + cos(y) = 0');
    grid on;
end
function dydt = nonlinear_ode(~, y)
    dydt = zeros(2, 1); % Initialize the output
    dydt(1) = y(2);     % y' = v
    dydt(2) = -cos(y(1)); % v' = -cos(y)
end

I hope this helps.

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Sam Chak 2024-6-2

Hi Manikanta,

Thank you for your clarification. The OP has updated the description of the problem, but there does not appear to be an edit history available for tracking the changes.

However, your efforts to be helpful are commendable. It is important to remain motivated, as some individuals may not be adept at framing their problems when asking questions for the first time. However, that does not necessarily imply that their questions are simply obvious homework assignments for students.