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Numerical ODE Methods
Undergraduate
Definition
Numerical ODE methods approximate solutions to differential equations that are difficult to solve analytically.
Formulas
y_n+1 = yₙ + h f(tₙ, yₙ)
Euler method (forward)
y_n+1 = yₙ + h f(tₙ + h/2, yₙ + (h)/(2)f(tₙ, yₙ))
Midpoint method (RK2)
Examples
Example 1
Solve dy/dt = y, y(0) = 1 using Euler method (h = 0.1).
Applications
Physics
Motion simulation
Engineering
Circuits, control systems
Biology
Population models
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