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- W2050591607 abstract "A unified approach is presented for proving the local, uniform and quadratic convergence of the approximate solutions and a-posteriori error bounds obtained by Newton's method for systems of nonlinear ordinary or partial differential equations satisfying an inverse-positive property. An important step is to show that, at each iteration, the linearized problem is inverse-positive. Many classes of problems are shown to satisfy this property. The convergence proofs depend crucially on an error bound derived previously by Rosen and the author for quasilinear elliptic, parabolic and hyperbolic problems." @default.
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- W2050591607 date "1979-08-01" @default.
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- W2050591607 title "Newton's method for nonlinear ordinary and partial differential equations" @default.
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- W2050591607 doi "https://doi.org/10.1016/0022-247x(79)90059-3" @default.
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