It is well known that a damped or underrelaxed Newton's method will sometimes solve a system of nonlinear equations when the full Newton's method cannot. This happens, for example, when only a poor ...

SIAM Journal on Numerical Analysis, Vol. 27, No. 3 (Jun., 1990), pp. 704-735 (32 pages) Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for ...

She’s right—using simultaneous equations does get really complicated, and if you’d like to send me your work for the solution, I’d love to see it. But the system is also kind of a trick. Like a sudoku ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Non-linear physics is the study of systems where the output is not directly proportional to the input. Unlike linear systems, which follow simple, predictable relationships, non-linear systems exhibit ...

A pruning reservoir computing technique can mitigate noise and reconstruct nonlinear dynamics for potential engineering and ...