Geodesic
A note on rapid convergence of approximate solutions for second order periodic boundary value problems
Archivum mathematicum, Tome 41 (2005) no. 2, pp. 135-143 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order $k$ $(k\ge 2)$.
In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order $k$ $(k\ge 2)$.
Classification : 34A45, 34B15, 34C25
Keywords: generalized quasilinearization; periodic boundary value problems; rapid convergence 
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     title = {A note on rapid convergence of approximate solutions for second order periodic boundary value problems},
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Khan, Rahmat A.; Ahmad, Bashir. A note on rapid convergence of approximate solutions for second order periodic boundary value problems. Archivum mathematicum, Tome 41 (2005) no. 2, pp. 135-143. http://geodesic.mathdoc.fr/item/ARM_2005_41_2_a0/

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