Question

​​​​​​​Rewrite equations (3), and (4a-c) in a form that allows you to implement Euler's Method. Your expressions should be in the final form

Vₘ₍ᵢ₊₁₎=
m₍ᵢ₊₁₎=
n₍ᵢ₊₁₎=
h₍ᵢ₊₁₎=

Answer 1

To implement Euler's method, we need to rewrite equations (3) and (4a-c) in the form Vₘ₍ᵢ₊₁₎= Vₘ₍ᵢ₎ + h × f(Vₘ₍ᵢ₎, tₘ₍ᵢ₎). Equations (3) and (4a-c) can be rewritten as: Vₘ₍ᵢ₊₁₎ = Vₘ₍ᵢ₎ + h × f₁(Vₘ₍ᵢ₎, tₘ₍ᵢ₎), m₍ᵢ₊₁₎ = m₍ᵢ₎ + h × f₂(m₍ᵢ₎, tₘ₍ᵢ₎), n₍ᵢ₊₁₎ = n₍ᵢ₎ + h × f₃(n₍ᵢ₎, tₘ₍ᵢ₎), and h₍ᵢ₊₁₎ = h₍ᵢ₎ + h × f₄(h₍ᵢ₎, tₘ₍ᵢ₎).

Step-by-step explanation:

To implement Euler's method, we need to rewrite the equations in the form: Vₘ₍ᵢ₊₁₎= Vₘ₍ᵢ₎ + h × f(Vₘ₍ᵢ₎, tₘ₍ᵢ₎). Let's rewrite equations (3) and (4a-c) accordingly:

(3): Vₘ₍ᵢ₊₁₎ = Vₘ₍ᵢ₎ + h × f₁(Vₘ₍ᵢ₎, tₘ₍ᵢ₎)

(4a-c): m₍ᵢ₊₁₎ = m₍ᵢ₎ + h × f₂(m₍ᵢ₎, tₘ₍ᵢ₎)

n₍ᵢ₊₁₎ = n₍ᵢ₎ + h × f₃(n₍ᵢ₎, tₘ₍ᵢ₎)

h₍ᵢ₊₁₎ = h₍ᵢ₎ + h × f₄(h₍ᵢ₎, tₘ₍ᵢ₎)