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Efficient Explicit Taylor ODE Integrators with Symbolic-Numeric Computing
Songchen Tan, Oscar Smith, Christopher Rackauckas
Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculatin…
Differentiable Programming for Differential Equations: A Review
Facundo Sapienza, Jordi Bolibar, Frank Schäfer +8
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Ma…
A Fully Adaptive Radau Method for the Efficient Solution of Stiff Ordinary Differential Equations at Low Tolerances
Shreyas Ekanathan, Oscar Smith, Christopher Rackauckas
Radau IIA methods, specifically the adaptive order Radau method in Fortran due to Hairer, are known to be state-of-the-art for the high-accuracy solution of highly stiff ordinary d…
NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
Avik Pal, Flemming Holtorf, Axel Larsson +6
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. Th…
Scalable higher-order nonlinear solvers via higher-order automatic differentiation
Songchen Tan, Keming Miao, Alan Edelman +1
This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives.…