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.
In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions to nonlinear differential equations used to model turbulence.
General Physics
Apr 16, 2026
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University of Birmingham experts have created open-source computer software that helps scientists understand how fast-moving particles behave when they interact with electromagnetic waves in space. Understanding how these ...
Space Exploration
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Scientists from Skoltech and the University of Potsdam have developed a physical theory that sheds light on how molecular motors organize the three-dimensional structure of the genome. Using theoretical polymer physics and ...
Molecular & Computational biology
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David J. Silvester, a mathematics professor at the University of Manchester, has developed a novel machine-learning method to detect sudden changes in fluid behavior, improving speed and the cost of identifying these instabilities ...
Soft Matter
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Heart to the left. Liver to the right. That's where you'll find these organs in a healthy human body, but surprisingly, in some people, the heart is on the right and the liver on the left. This normal or abnormal asymmetry ...
Cell & Microbiology
Mar 26, 2026
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25
The field of solar geoengineering revolves around the idea of cooling the globe via the injection of aerosols to reflect sunlight or to thin clouds. One such strategy, stratospheric aerosol injection (SAI), aims to mimic ...
Earth Sciences
Mar 23, 2026
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Animal studies often fail to predict human tissue responses to new drugs or newly developed therapies. Besides generating tremendous costs for clinical studies, it also raises significant ethical concerns. Therefore, novel ...
Cell & Microbiology
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A humble droplet can be an immensely useful tool for a number of fields, from medicine to manufacturing. Controlling the size of the droplet, though, is an important—and very tricky—task. With unprecedented precision, a team ...
Soft Matter
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15
An extensive computational study by researchers from Finland's University of Jyväskylä predicts that gold nanoclusters could selectively recognize chiral biomolecules. This property may help in detecting certain diseases ...
Bio & Medicine
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15
Most materials, especially metals and ceramics, are crystals. Their atoms are arranged in three-dimensional lattices that repeat the same exact pattern, over and over again. But there's a well-known saying in materials science: ...
Nanophysics
Mar 12, 2026
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