### Using matrix stability for variable telegraph partial differential equation

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Celik, C., & Duman, M.(2012). Crank- Nicolson method for the fractional diffusion equation with the Riesz fractional derivative. Journal of computational physics, 231(4), 1743-1750.

Gorial, I. I. (2011). Numerical methods for fractional reaction-dispersion equation with Riesz space fractional derivative. Engineering and Technology Journal, 29(4), 709-715.

Jafari, H., & Daftardar-Gejji, V. (2006). Solv- ing linear and nonlinear fractional diffusion and wave equations by Adomian decomposition. Applied Mathematics and Computation, 180(2), 488-497.

Karatay, I., Bayramoglu, S¸R., & S¸ahin, A. (2011). Implicit difference approximation for the time fractional heat equation with the nonlocal condition. Applied Numerical Mathematics, 61(12), 1281-1288.

Su, L., Wang, W., & Yang, Z. (2009). Finite difference approximations for the fractional advection-diffusion equation. Physics Letters A, 373(48), 4405-4408.

Tadjeran, C., Meerschaert, M. M., Scheffler, H.P.(2006). A second order accurate numerical approximation for the fractional diffusion equation. Journal of computational physics, 213(1), 205-213.

Nouy, A. (2010). A priori model reduction through proper generalized decomposition for solving time-dependent partial differ- ential equations. Computer Methods in Applied Mechanics and Engineering, 199(23-24), 1603-1626.

Wu, J. (1996). Theory and applications of partial functional differential equations, Springer-Verlag, New York.

Pontryagin, L. S. (2018). Mathematical theory of optimal processes, Routledge, London.

He, J. H. (2008). Recent development of the homotopy perturbation method. Topological methods in nonlinear analysis, 31(2), 205-209.

Holmes, E. E., Lewis, M. A., Banks, J. E., & Veit, R. R. (1994). Partial differential equations in ecology: spatial interactions and population dynamics. Ecology, 75(1), 17-29.

Dehghan, M., Shokri, A. (2008). A numerical method for solving the hyperbolic telegraph equation. Numerical Methods for Partial Differential Equations, 24(4), 1080-1093.

Faraj, B., & Modanli, M. (2017). Using difference scheme method for the numerical solution of telegraph partial differential equation. Journal of Garmian University, 3, 157-163.

Ashyralyev, A., & Modanli, M. (2015). An operator method for telegraph partial differential and difference equations. Boundary Value Problems, 41(1), 1-17.

Ashyralyev, A., & Modanli, M. (2015). Nonlocal boundary value problem for telegraph equations. AIP Conference Proceedings, 1676(1), 020078-1 - 020078-4.

Ashyralyev A, & Modanli, M. (2014). A numerical solution for a telegraph equation. AIP Conference Proceedings, 1611(1), 300-304.

Faraj, B. M. (2018). Difference scheme methods for telegraph partial differential equations. MSc Thesis. Harran University.

Smith, G. D. (1985). Numerical solution of partial differential equations: finite difference methods. Oxford university press.

Richtmyer, R. D., & Morton, K. W. (1994). Difference methods for initial-value problems, Krieger

DOI: http://dx.doi.org/10.11121/ijocta.01.2020.00870

### Refbacks

- There are currently no refbacks.

Copyright (c) 2020 Bawar Mohammed Faraj, Mahmut Modanli, Faraedoon Waly Ahmed

This work is licensed under a Creative Commons Attribution 4.0 International License.