Mathematical & Computational Physics
2 terms
Round-off Error
Mathematical & Computational Physics
Floating-Point Precision 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)
Runge-Kutta Methods
Mathematical & Computational Physics
Numerical ODE Integration Method
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)