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.
Researchers at University of Tsukuba have developed a technology for real-time estimation of the valence state and growth rate of iron oxide thin films during their formation. This novel technology was realized by analyzing ...
Condensed Matter
Oct 28, 2025
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Brazilian researchers have developed a technique that estimates the force exerted on each grain of sand in a dune from images. This method, which is based on numerical simulations and artificial intelligence (AI), transforms ...
Earth Sciences
Oct 23, 2025
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167
Shock waves should not be shocking—engineers across scientific fields need to be able to precisely predict how the instant and strong pressure changes initiate and dissipate to prevent damage. Now, thanks to a team from ...
General Physics
Oct 17, 2025
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Researchers from The University of New Mexico and Los Alamos National Laboratory have developed a novel computational framework that addresses a longstanding challenge in statistical physics.
General Physics
Sep 30, 2025
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50
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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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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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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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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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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155
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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