The numerical methods bible
Every method with its theory, its complete derivation embedded in the article, and solved, verified exercises. From errors and Taylor to nonlinear systems, in Spanish, Basque and English.
94 developed resources · 3 languages · verified calculations
Which numerical method should you use?
Describe your problem in two decisions. We give you a starting point, its limits, and the exact guide to apply it.
The nine topics
Each topic links theory, derivations and exercises together, wiki-style: start wherever you like.
Numerical foundations
Errors, significant figures, rounding, truncation, Taylor and order of approximation.
Interpolation
Newton, divided differences, Lagrange, Hermite, splines and error bounds.
Numerical differentiation
Forward, backward and central formulas, high accuracy and Richardson.
Numerical integration
Midpoint, trapezoid, Simpson, Newton-Cotes, Gauss-Legendre and multiple integration.
ODEs and initial value problems
Euler, Heun, Runge-Kutta, consistency, stability, convergence and first-order systems.
Multistep methods and stiffness
Adams-Bashforth, Adams-Moulton, predictor-corrector, implicit methods and stiff problems.
Linear systems
Residual, conditioning, Jacobi, Gauss-Seidel, spectral radius, convergence and SOR.
Nonlinear equations
Bisection, fixed point, Newton, secant, convergence order and high-order methods.
Nonlinear systems
Jacobian, Newton for systems, cost per iteration and high-order schemes.
Three ways in
Guides
The methods explained: motivation, theorems, formulas and their full derivation on the same page.
22Derivations
Every formula built step by step, no gaps: where it comes from, with what error and why it works.
31Solved exercises
Hand computations and numerical tables, solved to the end with verified numbers.