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.
Computational modeling could improve how scientists and planners understand and prepare for natural disasters on our coasts and even inland. In an article published in the International Journal of Mathematical Modelling and ...
Environment
Sep 2, 2025
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20
A qubit is the delicate, information-processing heart of a quantum device. In the coming decades, advances in quantum information are expected to give us computers with new, powerful capabilities and detectors that can pick ...
Quantum Physics
Aug 22, 2025
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70
A new numerical modeling tool developed by researchers at the University of Toronto could help improve the design and operation of intermittent water distribution systems, which supply more than a billion people around the ...
Environment
Aug 22, 2025
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27
In the ERC project HelixMold, a team from TU Graz developed a method for the computer-based design of artificial proteins, with a focus on custom biocatalysts for pharmaceutical applications or the degradation of biopolymers.
Biotechnology
Aug 7, 2025
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34
A five-dimensional (5D) Langevin approach developed by an international team of researchers, including members from Science Tokyo, accurately reproduces complex fission fragment distributions and kinetic energies in medium-mass ...
General Physics
Jun 18, 2025
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215
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
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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
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41
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
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