Geodesic
A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 99-117

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The paper is devoted to construction and justification of a nonuniform difference scheme with fourth order of accuracy for a two-dimensional boundary-value problem for an elliptic equation of second order in a domain with smooth curvilinear boundary. This scheme is called nonuniform because a stencil of difference operator alternates from node to node. In interior nodes a nine-point and standard five-point stencils are used. The special type of stencil is used near the boundary. The paper contains a description for constructing the scheme and for the proof accuracy. Numerical tests confirm the theoretical conclusions about the fourth order of accuracy for the approximate solution. 
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     author = {E. G. Bykova and V. V. Shaidurov},
     title = {A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {99--117},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/}
}
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E. G. Bykova; V. V. Shaidurov. A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 99-117. http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/