dorsal/arxiv
View SchemaQuasilinearization Approach to Nonlinear Problems in Physics with Application to Nonlinear ODEs
| Authors | V. B. Mandelzweig, F. Tabakin |
|---|---|
| Categories | |
| ArXiv ID | physics/0102041 |
| URL | https://arxiv.org/abs/physics/0102041 |
| DOI | 10.1016/S0010-4655(01)00415-5 |
Abstract
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the linear ones, and unlike perturbation theories is not based on the existence of some kind of a small parameter. It is shown that the quasilinearization method gives excellent results when applied to different nonlinear ordinary differential equations in physics, such as the Blasius, Duffing, Lane-Emden and Thomas-Fermi equations. The first few quasilinear iterations already provide extremely accurate and numerically stable answers.
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"abstract": "The general conditions under which the quadratic, uniform and monotonic\nconvergence in the quasilinearization method of solving nonlinear ordinary\ndifferential equations could be proved are formulated and elaborated. The\ngeneralization of the proof to partial differential equations is straight\nforward. The method, whose mathematical basis in physics was discussed recently\nby one of the present authors (VBM), approximates the solution of a nonlinear\ndifferential equation by treating the nonlinear terms as a perturbation about\nthe linear ones, and unlike perturbation theories is not based on the existence\nof some kind of a small parameter.\n It is shown that the quasilinearization method gives excellent results when\napplied to different nonlinear ordinary differential equations in physics, such\nas the Blasius, Duffing, Lane-Emden and Thomas-Fermi equations. The first few\nquasilinear iterations already provide extremely accurate and numerically\nstable answers.",
"arxiv_id": "physics/0102041",
"authors": [
"V. B. Mandelzweig",
"F. Tabakin"
],
"categories": [
"physics.comp-ph"
],
"doi": "10.1016/S0010-4655(01)00415-5",
"title": "Quasilinearization Approach to Nonlinear Problems in Physics with Application to Nonlinear ODEs",
"url": "https://arxiv.org/abs/physics/0102041"
},
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