🖥️
Finite Difference Method
★★★★☆Undergraduate
📖Definition
Finite difference method approximates derivatives with differences, converting differential equations to algebraic equations. Fundamental for numerical PDE solutions.
📐Formulas
f'(x) ≈ (f(x+h) - f(x))/(h)
Forward difference
f'(x) ≈ (f(x) - f(x-h))/(h)
Backward difference
f'(x) ≈ (f(x+h) - f(x-h))/(2h)
Central difference
f''(x) ≈ (f(x+h) - 2f(x) + f(x-h))/(h²)
Second derivative approximation
✏️Examples
예제 1
Approximate heat equation ∂u/∂t = α∂²u/∂x² with finite differences.
⚡Applications
CFD
Flow simulation
Heat Transfer
Temperature distribution
Structural Engineering
Stress analysis
🔗Related Documents
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#유한차분#PDE#finite difference#numerical PDE