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Compact Finite Difference Schematic Approach For Linear Second Order Boundary Value Problems
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Abstract
In this paper, we present a compact scheme of order four for the numerical solution of linear
second order boundary value problems. We also employ the finite difference approach to solve the
same problems. A comparison of the two approaches is shown with the help of three test problems. It
is found that the compact scheme is a powerful technique to solve the linear second order boundary
value problems as compared to the finite difference method.
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Polymer Engineering and Chemical Engineering, Materials Engineering, Physics, Chemistry, Mathematics
References
[1] Kreiss, H.O. 1975, Methods for the approximate solution of time dependent problems. GARP Report No. 13.
[2] Hirsh, R.S. 1975, Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique, Journal of Computational Physics, Vol. 19 (1). pp 90–109.
[3] Adam, Y. 1977, Highly accurate compact implicit methods and boundary conditions, Journal of Computational Physics, Vol. 24 (1). pp 10–22.
[4] Leventhal, S.H., Ciment, M. 1978, A note on the operator compact implicit method for the wave equation. Mathematics of Computation. Vol. 32 (1). pp 143-147.
[5] Dennis, S.C.R., Hudson, J.D. 1989, Compact finite-difference approximations to operators of Navier-Stokes type, Journal of Computational Physics. Vol. 85 (2). pp 390– 416. 4 h
[6] Ahmad, M.O.; An Exploration of Compact Finite Difference-methods for Numerical Solution of PDE, Ph.D. Thesis, University of Western, Ontario, Canada, (1997).
[7] Burden, R.L., Faires, J.D. 2010, Numerical Analysis. International Thomson Publishing Inc, New York, USA.
[2] Hirsh, R.S. 1975, Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique, Journal of Computational Physics, Vol. 19 (1). pp 90–109.
[3] Adam, Y. 1977, Highly accurate compact implicit methods and boundary conditions, Journal of Computational Physics, Vol. 24 (1). pp 10–22.
[4] Leventhal, S.H., Ciment, M. 1978, A note on the operator compact implicit method for the wave equation. Mathematics of Computation. Vol. 32 (1). pp 143-147.
[5] Dennis, S.C.R., Hudson, J.D. 1989, Compact finite-difference approximations to operators of Navier-Stokes type, Journal of Computational Physics. Vol. 85 (2). pp 390– 416. 4 h
[6] Ahmad, M.O.; An Exploration of Compact Finite Difference-methods for Numerical Solution of PDE, Ph.D. Thesis, University of Western, Ontario, Canada, (1997).
[7] Burden, R.L., Faires, J.D. 2010, Numerical Analysis. International Thomson Publishing Inc, New York, USA.