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There is a debate about the status of computation within the scientific method. [4] Sometimes it is regarded as more akin to theoretical physics; some others regard computer simulation as "computer experiments", [4] yet still others consider it an intermediate or different branch between theoretical and experimental physics, a third way that supplements theory and experiment.
Ross–Fahroo pseudospectral method — class of pseudospectral method including Chebyshev, Legendre and knotting; Ross–Fahroo lemma — condition to make discretization and duality operations commute; Ross' π lemma — there is fundamental time constant within which a control solution must be computed for controllability and stability
The following is a list of notable unsolved problems grouped into broad areas of physics. [1]Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.
In applied mathematics, the numerical sign problem is the problem of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral.
Contains a brief, engineering-oriented introduction to FDM (for ODEs) in Chapter 08.07. John Strikwerda (2004). Finite Difference Schemes and Partial Differential Equations (2nd ed.). SIAM. ISBN 978-0-89871-639-9. Smith, G. D. (1985), Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed., Oxford University Press
In numerical analysis, leapfrog integration is a method for numerically integrating differential equations of the form ¨ = = (), or equivalently of the form ˙ = = (), ˙ = =, particularly in the case of a dynamical system of classical mechanics.
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as " numerical integration ", although this term can also refer to the computation of integrals .