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.

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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 $k$ $(k\ge 2)$.
Classification : 34A45, 34B15, 34C25
Keywords: generalized quasilinearization; periodic boundary value problems; rapid convergence 
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     author = {Khan, Rahmat A. and Ahmad, Bashir},
     title = {A note on rapid convergence of approximate solutions for second order periodic boundary value problems},
     journal = {Archivum mathematicum},
     pages = {135--143},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2005},
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     zbl = {1117.34018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005__41_2_a0/}
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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/