AI techniques excel at solving complex equations in physics, especially inverse problems

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...
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Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients

Mathematics of Computation, Vol. 49, No. 180 (Oct., 1987), pp. 523-542 (20 pages) We present Runge-Kutta methods of high accuracy for stochastic differential ...
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New AI techniques to solve complex equations in physics

Researchers from the Institute of Cosmos Sciences of the University of Barcelona (ICCUB) have developed a new framework based ...
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Solution of Jump Parameter Systems of Differential and Difference Equations with Semi-Markov Coefficients

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two ...
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Numerical simulation and applications of the convection–diffusion–reaction equation with the radial basis function in a finite-difference mode

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...