The article discusses the development and evaluation of numerical algorithms designed for solving nonlinear equations, benchmarking against established solvers like NLsolve.jl and Sundials. Key sections cover the algorithms' mathematical descriptions, globalization strategies, and sensitivity analyses. Special capabilities include smart algorithm defaults and non-allocating static algorithms. The results highlight the robustness of the proposed solvers on 23 test problems, showcasing their adaptability to different problem difficulties. Notably, the use of Automatic Differentiation in the Julia implementation differs from previous FORTRAN90 approaches, illustrating advancements in computational techniques for nonlinear problem-solving.
We evaluate our solvers on three numerical experiments and benchmark them against other nonlinear equation solvers like NLsolve.jl and Sundials.
The robustness of our approach is tested on a suite of 23 small nonlinear systems, each posing varying degrees of difficulty for solver evaluation.
In contrast to the FORTRAN90 version of the test suite, our pure Julia version relies on Automatic Differentiation or Finite Differencing to compute Jacobians.
Our experiments demonstrate that our numerical algorithms show promising results in handling the complexities of nonlinear equations effectively.
#nonlinear-equations #numerical-algorithms #benchmarking #automatic-differentiation #computational-techniques
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