I am a Matlab rookie. I need to solve numerically the following second order differential equations(adsbygoogle = window.adsbygoogle || []).push({});

d^2x/dt^2 + w0_(el) * x = e/m_e * E - K3/m_e * x *y;

d^2y/dt^2 + w0_(v) * y = - K_3/2M * x^2;

I have started to deal with only the harmonic part of the problem. So I tried to solve

d^2x/dt^2 + w0_(el) * x

d^2y/dt^2 + w0_(v) * y

with the following program

t = 0:10^(-15):0.5*10^(-9);

x0 = zeros(1,2);

x0(1) = input('Insert the initial value of x');

x0(2) = input('Insert the initial value of dx/dt');

[t, x] = ode45(@harmonic, t, x0);

plot(t, x(:, 1), 'g')

title('Electronic position vs time'), xlabel('Time '),

ylabel('Position')

hold

figure

plot(t, x(:, 2), 'b')

title('Nucleus position vs time'), xlabel('Time '),

ylabel('Position')

where the function "harmonic" is

function ydot = harmonic(t, x)

ydot = zeros(2,1);

w_e = 10^30;

w_v = 10^24;

ydot(1) = x(3);

ydot(2) = x(4);

ydot(3) = -w_e*x(1);

ydot(4) = -w_v*x(2);

The outcome is a damping oscillation behaviour for x, which is of course meaningless because there aren't damping terms in the harmonic equations. So I am pretty desperate, if someone can help me I wuold be very glad.

Thank you!

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# Help with Matlab solving second order differential equations

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