Author(s) Fatmah M. Alabdali, Huda Omar Bakodah

Affiliation(s)
Department of Mathematics Science Faculty for Girls, King Abdulaziz University, Jeddah, KSA.

ABSTRACT

A new modification of the Method of Lines is proposed for the solution of first order partial differential equations. The accuracy of the method is shown with the matrix analysis. The method is applied to a number of test problems, on uniform grids, to compare the accuracy and computational efficiency with the standard method.

KEYWORDS
Method of Lines, First-Order Hyperbolic Equation, Numerical Solution

Cite this paper
Alabdali, F. and Bakodah, H. (2014) A New Modification of the Method of Lines for First Order Hyperbolic PDEs. Applied Mathematics, 5, 1457-1462. doi: 10.4236/am.2014.510138.

References
[1]   Smith, G.D. (1985) Numerical Solution of Partial Differential Equations (Finite Difference Methods). 3rd Edition, Oxford University Press, Oxford.

[2]   Schiesser, W.E. (1978) The Numerical Method of Lines: Integration of Partial Differential Equations. 2nd Edition, Clarendon Presses, Oxford.

[3]   Sharaf, A.A. and Bakodah, H.O. (2005) A Good Spatial Discretization in the Method of Lines. Applied Mathematics and Computation, 171-172, 1253-1263.

[4]   Carver, M.B. and Hinds, H.W. (1978) The Method of lines and the Advective Equation. Simulation, 31, 59-69.