I have to simulate the motion of particle in an electromagnetic device which deflects particle using electric and magnetic field. Those field are arranged in such a way that the electric field is inside the magnetic one. Moreover the electrodes begin at the center of the magnetic field ad their end is a bit outside the coils. The motion equations are: 1) d^2x(z)/dz^2 = qE/mv^2 2) d^2y(z)/dz^2 = qB/mv The problem is that MatLab cannot solve second order differential equation, thus I have tried to use the code: Code (Text): %%Initial drift rhsE1=@(z,x)[x(2); 0]; [zaE1, xaE1] = ode45(rhsE1, [0 69], [0 0]); %%inside E field E=1; rhsE =@(z,x)[x(2); (q/m)*(E/v^2)]; [zaE, xaE] = ode45(rhsE, [70 130], [0 0]); For the drift after the field I have calculated the derivative of the trajectory and used it as initial condition for solving the eqaution of motion in the drift sector. I have also write a similar code for the magnetic field. The problem is that solving the equation separately doesn't seem to me correct because one solution could be longer than the other... I have also tryed to solve the lorentz force using the code: Code (Text): %%%% f = @(t,y) [y(4:6); (q_over_m).*cross(y(4:6),B)+(q_over_m).*E]; [t,y] = ode23t(f,tspan,y0); %%% and some "while" loop like: Code (Text): %%% while (z>= length at which B begins || z<= length atwhich the electric field begins) B=[1 0 0]'; E = [0 0 0]'; solve the equation z=y(end,3); end %%%%% and so on... The problem is that the code is incredibly slow and sometimes, I think, it cannot get out of a loop. I think I have used bad approaches to solve the problem, someone can give me a clue?