%0 Journal Article
%T An O(hk5) accurate finite difference method for the numerical
	solution of fourth order two point boundary value problems on geometric meshe
%A Jha, Navnit
%A Bieniasz, Lesław K.
%J Czasopismo Techniczne
%V 2016
%R 10.4467/2353737XCT.16.139.5718
%N Nauki Podstawowe Zeszyt 1-NP 2016
%P 55-72
%K Geometric mesh, finite difference method, compact scheme, singularity, stiff equations, Korteweg-de Vries equation, maximum absolute errors
%@ 0011-4561
%D 2016
%U https://ejournals.eu/czasopismo/czasopismo-techniczne/artykul/an-o-hk5-accurate-finite-difference-method-for-the-numerical-solution-of-fourth-order-two-point-boundary-value-problems-on-geometric-meshe
%X 
	Two point boundary value problems for fourth order, nonlinear, singular and non-singular ordinary differential equations occur in various areas of science and technology. A compact, three point finite difference scheme for solving such problems on nonuniform geometric meshes is presented. The scheme achieves a fifth or sixth order of accuracy on geometric and uniform meshes, respectively. The proposed scheme describes the generalization of Numerov-type method of Chawla (IMA J Appl Math 24:35-42, 1979) developed for second order differential equations. The convergence of the scheme is proven using the mean value theorem, irreducibility, and monotone property of the block tridiagonal matrix arising for the scheme. Numerical tests confirm the accuracy, and demonstrate the reliability and efficiency of the scheme. Geometric meshes prove superior to uniform meshes, in the presence of boundary and interior layers.