Geodesic
An effective method for numerical solution and numerical derivatives for sixth order two-point boundary value problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5

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In this paper, we study an effective quintic polynomial spline method for numerical solution, and first order to fifth order numerical derivatives of the analytic solution at the knots for a class of sixth order two-point boundary value problems. Our new method is based on a quintic spline interpolation problem. It is easy to implement and is able to provide sixth order accurate numerical results at the knots. Numerical tests show that our method is very practical and effective. 
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     author = {Feng-Gong Lang and Xiao-Ping Xu},
     title = {An effective method for numerical solution and numerical derivatives for sixth order two-point boundary value problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {822},
     publisher = {mathdoc},
     volume = {55},
     number = {5},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a6/}
}
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Feng-Gong Lang; Xiao-Ping Xu. An effective method for numerical solution and numerical derivatives for sixth order two-point boundary value problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a6/