Abstract
Among the popular and successful techniques for solving boundary-value problems for nonlinear, ordinary differential equations (ODE) are quasilinearization and the Galerkin procedure. In this note, it is demonstrated that utilizing the Galerkin criterion followed by the Newton-Raphson scheme results in the same iteration process as that obtained by applying quasilinearization to the nonlinear ODE and then the Galerkin criterion to each linear ODE in the resulting sequence. This equivalence holds for only the Galerkin procedure in the broad class of weighted-residual methods.
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References
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Communicated by R. E. Kalaba
This work was supported in part by the National Science Foundation, Grant No. GJ-1075.
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Neuman, C.P., Sen, A. Galerkin's procedure, quasilinearization, and nonlinear boundary-value problems. J Optim Theory Appl 9, 433–437 (1972). https://doi.org/10.1007/BF00934742
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DOI: https://doi.org/10.1007/BF00934742