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Civil-Comp Proceedings
ISSN 1759-3433
ISSN 1759-3433
CCP: 26
ADVANCES IN COMPUTATIONAL MECHANICS
ADVANCES IN COMPUTATIONAL MECHANICS
Edited by: M. Papadrakakis and B.H.V. Topping
Paper X.1
Accuracy Increase of Finite Difference Calculations by Means of Differentiation of the Partial Differential Equations and the Boundary Conditions
M. Arad, R. Segev and G. Ben-Dor
Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Full Bibliographic Reference for this paper
M. Arad, R. Segev, G. Ben-Dor, "Accuracy Increase of Finite Difference Calculations by Means of Differentiation of the Partial Differential Equations and the Boundary Conditions", in M. Papadrakakis, B.H.V. Topping, (Editors), "Advances in Computational Mechanics", Civil-Comp Press, Edinburgh, UK, pp 343-351, 1994. doi:10.4203/ccp.26.10.1
Abstract
A numerical algorithm for producing high-order solutions
for equilibrium problems is presented. The approximated
solutions are improved by differentiating both the governing
partial differential equations and their boundary conditions. The
advantages of the proposed method over standard finite
difference methods are: the possibility of using arbitrary
meshes and an improvement in approximating the boundary
conditions. Furthermore, the proposed method is capable of
reaching approximate solutions which are more accurate than
other finite difference methods, when the same number of
nodal points participate in the local scheme. Calculations based
on the proposed method and on another finite difference
method are compared to analytical results. The comparison
clearly illustrates the superiority of the proposed method.
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