MATLAB: How to solve difference equation in MATLAB

difference equation

How to solve the difference equation for

yn+1 =5/2 yn +yn-1 ,y0 =y1 =1 in terms of the roots of its characteristic equation in MATLAB ?

Best Answer

An alternative is to use filter()

a = [1 -5/2 -1];
b = 0;
ic = [1 1];
n = 50; % 50 terms
y1 = [ic(1) filter(b, a, ones(1, n-1), ic)];

Related Solutions

MATLAB: 2nd order systems of differential equation

By adding 3 variables y4,y5 and y6 your system becomes a first order differential equations system.

%y4=dy1/dt, thus d2y1/dt2=dy4/dt
%y5=dy2/dt, thus d2y2/dt2=dy5/dt
%y6=dy3/dt, thus d2y3/dt2=dy6/dt
%The system of equation becomes
%dy1/dt=y11; 
%dy2/dt=y22; 
%dy3/dt=y33;
%dy4/dt+5*y4+y2^2-y1=0;
%dy5/dt+5*y5+y3^2-y2=0;
%dy6/dt+5*y6-y3=0;

% which can be programmed

function dy=myequ(t,y)
dy(1)=y(4)
dy(2)=y(5)
dy(3)=y(6)
dy(4)=-5*y4-y2^2+y1
dy(5)=-5*y5-y3^2+y2
dy(6)=-5*y6+y3

% you can call myequ

tspan=[0 10];
y0=[1 0 1 0 1 1]; % Initial conditions
[t,y]=ode45(@myequ,tspan,y0)

MATLAB: Solving system of ODE using ode45 in matlab

clc

clear

n = 30;

t = [0 0.52 1.04 1.75 2.37 3.25 3.83]';

x = [153 185 208 249 261 271 273]';

tt = linspace(t(1),t(end),n);

xx = spline(t,x,tt);

v = calc_derv(tt,xx);

a = calc_derv(tt,v);

subplot(2,1,1),plot(tt,v)

title('Jet Fighters Velocity')

xlabel('Time (s)')

ylabel('Velocity (m/s)')

subplot(2,1,2),plot(tt,a)

title('Jet Fighters Acceleration')

xlabel('Time (s)')

ylabel('Acceleration (m/s^2)')

% calculate 1st order derivative using finite differences

function dydx = calc_derv(x,y);

n = length(x);

h = x(2)-x(1);

dydx(1) = (-y(3) + 4*y(2) - 3*y(1))/(2*h);

dydx(n) = (3*y(n) - 4*y(n-1) + y(n-2))/(2*h);

for i = 2:n-1

dydx(i) = (y(i+1) - y(i-1))/(2*h);

end

Best Answer

Related Solutions

MATLAB: 2nd order systems of differential equation

MATLAB: Solving system of ODE using ode45 in matlab

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