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When one does not know the exact solution, one may look for the approximation with small residual. Residuals appear in many areas in mathematics, including iterative solvers such as the generalized minimal residual method, which seeks solutions to equations by systematically minimizing the residual.
Matrix analysis; Merged CORDIC; Mesh generation; Meshfree methods; Method of fundamental solutions; Method of dominant balance; Miller's recurrence algorithm; Minimax approximation algorithm; Minimum polynomial extrapolation; Model order reduction; Modulus of smoothness; Momentum mapping format; Monte Carlo method; Movable cellular automaton ...
Modal analysis using FEM — solution of eigenvalue problems to find natural vibrations; Céa's lemma — solution in the finite-element space is an almost best approximation in that space of the true solution; Patch test (finite elements) — simple test for the quality of a finite element
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones.
Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic-matrix-and-graph theory. Other areas of computational mathematics include computer algebra and symbolic computation .
(Extensive online material on ODE numerical analysis history, for English-language material on the history of ODE numerical analysis, see, for example, the paper books by Chabert and Goldstine quoted by him.) Pchelintsev, A.N. (2020). "An accurate numerical method and algorithm for constructing solutions of chaotic systems".