Geodesic
Modification of finite differences method with use of~Taylor expansions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 152-162

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The conducted research compares the method of Taylor expansions and the finite difference method. The obtained method of Taylor expansions employs three, four and five series terms. For each modification a finite difference scheme is presented and its stability, convergence, and approximation are analyzed. For both methods the number of arithmetic operations is counted and compared as well as an error. The advantages of the method of Taylor expansions are revealed.
Keywords: ordinary differential equations, boundary value problem, Taylor series, approximation, stability, finite difference method, method of Taylor expansions, numerical method.
Mots-clés : convergence 
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     author = {G. A. Pavlova and I. V. Belyaeva},
     title = {Modification of finite differences method with use {of~Taylor} expansions},
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     pages = {152--162},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a14/}
}
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G. A. Pavlova; I. V. Belyaeva. Modification of finite differences method with use of~Taylor expansions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 152-162. http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a14/