TY - JOUR
TI - An O(hk5) accurate finite difference method for the numerical
	solution of fourth order two point boundary value problems on geometric meshe
AU - Jha, Navnit
AU - Bieniasz, Lesław K.
TI - An O(hk5) accurate finite difference method for the numerical
	solution of fourth order two point boundary value problems on geometric meshe
AB - 
	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.
VL - 2016
IS - Fundamental Sciences Issue 1-NP 2016
PY - 2016
SN - 0011-4561
C1 - 2353-737X
SP - 55
EP - 72
DO - 10.4467/2353737XCT.16.139.5718
UR - https://ejournals.eu/en/journal/czasopismo-techniczne/article/an-o-hk5-accurate-finite-difference-method-for-the-numerical-solution-of-fourth-order-two-point-boundary-value-problems-on-geometric-meshe
KW - Geometric mesh
KW - finite difference method
KW - compact scheme
KW - singularity
KW - stiff equations
KW - Korteweg-de Vries equation
KW - maximum absolute errors