An Accurate Finite-Difference Method for 1-D Wave Problem Based on a Pre-Concerted Grid
Valmir BAME , Lulezim HANELLI
An accurate numerical method is proposed for the solution of 1-D initial-boundary value wave problem. It is of finite-difference type, where a pre-concerted grid is constructed using a specific time discretization. The ultimate goal is the minimizing of global error. Keeping of the stability-accuracy balance is the key element of the new proposal. It is particularly useful in case of large integration domains. The most important part of the method is implemented and tested in Matlab, and the results are compared with those of classic difference method.
Initial-boundary value wave problem, Triangle of determinacy, Stability limit, Stability threshold, Non-uniform grid.
 Burden, R.L. and Faires, J.D. and Reynolds, A.C. 2007. Numerical Analysis. Prindle, Weber & Schmidt, Massachusetts 02116
 Falk, J. and Tessmer, D. and Gajewski, D. 1998. Efficient finite-difference modelling of seismic waves using locally adjustable time steps. Geophysical Prospecting, 46:603-616.
 Huang, C. and Dong, L. 2009. Staggered-Grid High-Order Finite-Difference Method in Elastic Wave Simulation with Variable Grids and Local Time-Steps. Chinese Journal of Geophysics. 52. 10.1002/cjg2.1457.
 Igel, Heiner & Käser, Martin & Stupazzini, Marco. 2010. Seismic Wave Propagation in Media with Complex Geometries, Simulation of. 10.1007/978-1-4419-7695-6_41.
 Madariaga, R. 1976. Dynamics of an expanding circular fault. Bull. Seism. Soc. Am., 1976, 66(3): 639∼666.
 Tyn Myint-U, T. and Debnath, L. 2007. Linear partial differential equations for scientists and engineers, Birkhauser Boston, New York.
[Valmir BAME , Lulezim HANELLI (2019) An Accurate Finite-Difference Method for 1-D Wave Problem Based on a Pre-Concerted Grid IJIRCST Vol-6 Issue-5 Page No-44-49] (ISSN 2347 - 5552). www.ijircst.org
Department of Mathematics, University "Aleksander Moisiu", Durres, Albania, firstname.lastname@example.org