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Mathematical & Computational Physics

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Mathematical & Computational Physics

Round-off Error

The difference between the exact mathematical value of a function and the value computed using finite-precision floating-point arithmetic.

Machine Epsilon ε_mach ≈ 2⁻⁵³ ≈ 1.11 × 10⁻¹⁶ (IEEE 754 Double Precision) Floating-Point Precision Error Mathematical & Computational Physics

Runge-Kutta Methods

A family of iterative numerical integration algorithms used to solve ordinary differential equations with high accuracy.

RK4: y_(n+1) = y_n + (h / 6) (k₁ + 2 k₂ + 2 k₃ + k₄) Numerical ODE Integration Method