A University of New South Wales (UNSW) Sydney mathematician has revealed the first successful solution of an ‘impossible’ equation once considered unsolvable. Described as algebra’s oldest problem, ...

Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and ...

Artifitial Neural Networks for Solving Ordinary and Partial Differential Equations, in this case, Schrodinger's Equation for One Particle in a 1-Dimentional Box This is a project done as a partial ...

Abstract: The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e., Lyapunov functionals, for a linear time-delay system with a constant and a ...

The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both ...

Last year, MIT developed an AI/ML algorithm capable of learning and adapting to new information while on the job, not just during its initial training phase. These “liquid” neural networks (in the ...

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Abstract: Initial boundary-value problem for the homogeneous wave equation with dynamic boundary condition is considered in three-dimensional Lipschitz domain. The Kirchhoff's formula is used to ...

Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity ...