Numerical Methods for DEs - Theory & Concepts

Solving differential equations using numerical approximations, including Euler's method, Runge-Kutta methods, and error analysis.

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Numerical Methods Comparison

Solving $y' = y$ with $y(0)=1$ .

Compare the simple Euler method (1st order) to the Runge-Kutta method (4th order). Notice how much faster RK4 converges to the exact solution as step size $h$ decreases.

Step Size (

h

)1.00

Fine (0.1)Coarse (1.5)

Exact (

e^x

)

Euler's MethodE ~ O(h)

RK4 MethodE ~ O(h^4)

x ∈ [0, 3]

First-Order DEs (Separable & Homogeneous) - Theory & Concepts - First Order Separable And Homogeneous Exact & Linear Differential Equations - Theory & Concepts - Exact And Linear Equations Applications of First-Order DEs - Theory & Concepts - Applications Of First Order Des Higher-Order Homogeneous DEs - Theory & Concepts - Higher Order Homogeneous Equations

Numerical Methods Comparison

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