Numerical techniques are computational methods for approximating solutions to mathematical problems that lack closed-form expressions or are analytically intractable. They encompass algorithms for root finding, numerical integration and differentiation, solution of linear and nonlinear systems, eigenvalue problems, optimization, and numerical solution of ordinary and partial differential equations. These techniques rely on discretization, iteration, and error analysis, with careful attention to stability, convergence, conditioning, and computational complexity. They are implemented using floating-point arithmetic and often exploit matrix factorizations, interpolation, finite difference, finite element, or spectral methods to achieve controllable accuracy within specified tolerances.
A pioneering method to simulate how nanoparticles move through the air could boost efforts to combat air pollution, suggests a study in the Journal of Computational Physics.
Nanophysics
May 27, 2025
0
45
In nature and technology, crystallization plays a pivotal role, from forming snowflakes and pharmaceuticals to creating advanced batteries and desalination membranes. Despite its importance, crystallization at the nanoscale ...
A pair of physicists at Universidad Nacional de Mar del Plata, in Argentina, have created a computer simulation of the famed Antikythera Mechanism and in so doing have found that manufacturing inaccuracies may have caused ...
AI has created a sea change in society; now, it is setting its sights on the sea itself. Researchers at Osaka Metropolitan University have developed a machine learning-powered fluid simulation model that significantly reduces ...
General Physics
Apr 3, 2025
0
40
Researchers, including those from the University of Tokyo, developed Deep Nanometry, an analytical technique combining advanced optical equipment with a noise removal algorithm based on unsupervised deep learning.
Bio & Medicine
Feb 20, 2025
0
112
Figuring out certain aspects of a material's electron structure can take a lot out of a computer—up to a million CPU hours, in fact. A team of Yale researchers, though, are using a type of artificial intelligence to make ...
Condensed Matter
Dec 19, 2024
0
125
How does the Earth generate its magnetic field? While the basic mechanisms seem to be understood, many details remain unresolved. A team of researchers from the Center for Advanced Systems Understanding at the Helmholtz-Zentrum ...
Planetary Sciences
Dec 16, 2024
0
97
For human researchers, it takes many years of work to discover new super-resolution microscopy techniques. The number of possible optical configurations of a microscope—for example, where to place mirrors or lenses—is enormous.
Optics & Photonics
Dec 10, 2024
0
128
A joint research team led by Yuuki Kubo and Shiji Tsuneyuki of the University of Tokyo has developed a new computational method that can efficiently determine the crystal structures of multiphase materials, powders that contain ...
Condensed Matter
Dec 5, 2024
0
108
When laser energy is deposited in a target material, numerous complex processes take place at length and time scales that are too small to visually observe. To study and ultimately fine-tune such processes, researchers look ...
Condensed Matter
Nov 25, 2024
0
59
