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Bohan Li, Class 9am-9:50am
20/02/2020
Euler’s Method for Systems of ODEs
Euler’s method is a first-order numerical method for solving the ordinary differential equations
(ODEs) for a given initial condition.
The system of ordinary differential equations are:
The Susceptible Equation
ds
= −bs(t)i(t)
(1)
dt
The Infected Equation
di
= bs(t)i(t) − ki(t)
dt
(2)
The constants and the initial conditions are b = 21 , k = 13 and s(0) = 1, b = 1.27 × 10−6 .
A step size of ∆t = 10 is taken and the solution of (1) and (2) obtained in the graphical form is:
On analyzing solution of the ODEs by Euler’s method and comparing with the exact solution,
the solution obtained by Euler’s method is not exact. The susceptible fraction of population
after 100 days reaches to 0.4 while the solution obtained through Euler’s method is not giving
the same result. This is due to the step size chosen. The step size of ∆t = 10 is very large.
Similarly, the infection fraction obtained by the Euler’s solution is reaching a maximum of 2
which is not possibl...