This work deals with a second order linear general equation with partial derivatives for a two-variable function. It covers a wide range of applications. This equation is solved with a finite difference hybrid method: BTCS + CTCS. This scheme is simple, precise, and economical in terms of time and space occupancy in memory.
References
[1]
Kuneš, J. (2012) Similarity and Modeling in Science and Engineering. Cambridge International Science Publishing, 131-141.
[2]
Gurarslan, G., Karahan, H., Alkaya, D., Sari, M. and Yasar, M. (2013) Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method. Mathematical Problems in Engineering, 2013, Article ID: 672936.
https://doi.org/10.1155/2013/672936
[3]
Crank, J. and Nicolson, P. (1947) A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type. Proceedings of the Cambridge Philosophical Society, 43, 50-67.
https://doi.org/10.1017/S0305004100023197
[4]
Mittal, R.C. and Bhatia, R. (2013) Numerical Solution of Second Order One Dimensional Hyperbolic Telegraph Equation by Cubic B-Spline Collocation Method. Applied Mathematics and Computation, 220, 496-506.
https://doi.org/10.1016/j.amc.2013.05.081
[5]
Inc, M., Akgül, A. and Kiliüman, A. (2013) Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method. Abstract and Applied Analysis, 2013, Article ID: 768963.
https://doi.org/10.1155/2013/768963
[6]
Pandit, S., Kumar, M. and Tiwari, S. (2015) Numerical Simulation of Second-Order Hyperbolic Telegraph Type Equations with Variable Coefficients. Computer Physics Communications, 187, 83-90. https://doi.org/10.1016/j.cpc.2014.10.013
[7]
Lakestani, M. and Saray, B.N. (2010) Numerical Solution of Telegraph Equation Using Interpolating Scaling Functions. Computers and Mathematics with Applications, 60, 1964-1972. https://doi.org/10.1016/j.camwa.2010.07.030
Engeln-Muellges, G. and Reutter, F. (1991) Formelsammlung zur Numerischen Mathematik mit QuickBasic-Programmen. Dritte Auflage, BI-Wissenchaftsverlag, 472-481.
[10]
Conte, S.D. and de Boor, C. (1981) Elementary Numerical Analysis: An Algorithmic Approach. 3rd Edition, McGraw-Hill, New York, 153-157.
[11]
Usmani, R.A. (1994) Inversion of a Tridiagonal Jacobi Matrix. Linear Algebra and Its Applications, 212-213, 413-414. https://doi.org/10.1016/0024-3795(94)90414-6
[12]
Gueye, S.B. (2014) Semi-Analytical Solution of the 1D Helmholtz Equation, Obtained from Inversion of Symmetric Tridiagonal Matrix. Journal of Electromagnetic Analysis and Applications, 6, 425-438. https://doi.org/10.4236/jemaa.2014.614044
[13]
Hu, G.Y. and O’Connell, R.F. (1996) Analytical Inversion of Symmetric Tridiagonal Matrices. Journal of Physics A, 29, 1511-1513.
https://doi.org/10.1088/0305-4470/29/7/020
[14]
da Fonseca, C.M. and Petronilho, J. (2001) Explicit Inverses of Some Tridiagonal Matrices. Linear Algebra and Its Applications, 325, 7-21.