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NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia

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arxiv 2403.16341 v3 pith:BTD4HAP7 submitted 2024-03-25 math.NA cs.NA

Avik Pal , Flemming Holtorf , Axel Larsson , Torkel Loman , Utkarsh , Frank Schäefer , Qingyu Qu , Alan Edelman
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Chris Rackauckas
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classification math.NAcs.NA
keywords nonlinearsolvenonlinearequationsautomatichigh-performanceimplementedjulialanguage
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Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for GPU-accelerated computation through static array kernels, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as PETSc SNES, Sundials KINSOL, and MINPACK, NonlinearSolve.jl demonstrates robustness and efficiency, achieving significant advancements in solving nonlinear equations while being implemented in a high-level programming language. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 7 citations worldwide. Full citation record

  1. FractionalDiffEq.jl: High Performance Fractional Differential Equation Solver in Julia

    math.NA 2025-06 conditional novelty 6.0 of 10

    A new Julia package, FractionalDiffEq.jl, implements multiple fractional ODE solvers and claims superior speed and stability over existing FDE toolkits in benchmarks.

  2. Scalable higher-order nonlinear solvers via higher-order automatic differentiation

    math.NA 2025-01 conditional novelty 5.0 of 10

    Using Taylor-mode automatic differentiation, the authors implement scalable Halley's method for nonlinear systems and report speedups over Newton's method on dense, sparse, and ODE-internal solves.

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