Hey @MINATI
To replace the code xSol(t) = simplify(xSol(t)) or pretty([xSol(t); ySol(t)]) from “dsolve” with “bvp4c”, you would typically solve a boundary value problem (BVP) instead of an initial value problem (IVP).
Kindly follow the example on how to set up and solve a BVP using “bvp4c”:
1. Define the ODE as a system of first-order equations.
function dydx = bvpfcn(x, y)
dydx = zeros(2, 1); % Initialize the output
dydx(1) = y(2); % y1' = y2
dydx(2) = -y(1); % y2' = -y1 (example equation)
end
2. Specify the boundary conditions.
function res = bcfcn(ya, yb)
res = [ya(1); yb(1) - 2]; % y(0) = 0, y(1) = 2
end
3. Create an initial guess for the solution.
xmesh = linspace(0, 1, 5); % Mesh points
solinit = bvpinit(xmesh, [0; 0]); % Initial guess for y and y'
4. Use bvp4c to solve the problem.
sol = bvp4c(@bvpfcn, @bcfcn, solinit);
5. Plot the solution to visualise the results.
plot(sol.x, sol.y(1,:), '-o'); % Plot y1
xlabel('x');
ylabel('y');
title('Solution of the BVP');
For more information on “bvp4c”, kindly refer the following MATLAB documentation:
