In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.

Mathematical definition

be a well-posed problem is a real or complex functional relationship, defined on the Cartesian product, such that exists a locally lipschitz called resolvent. We define numerical method, the sequence of problems

. The problems of which the method consists need not be well-posed. If they are, the method is said to be stable or well-posed.

Consistency

. So, a numerical method is called consistent of its solutions:

the method is said to be strictly consistent.

Convergence

a sequence of admissible perturbations is convergence:

implies the convergence of the associated method.

See also

• Numerical methods for ordinary differential equations

• Numerical methods for partial differential equations

References