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Block Unification Scheme for Elliptic, Telegraph, and Sine-Gordon Partial Differential Equations

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DOI: 10.4236/ajcm.2015.52014    4,500 Downloads   4,880 Views   Citations
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ABSTRACT

In this paper, we use the method of lines to convert elliptic and hyperbolic partial differential equations (PDEs) into systems of boundary value problems and initial value problems in ordinary differential equations (ODEs) by replacing the appropriate derivatives with central difference methods. The resulting system of ODEs is then solved using an extended block Numerov-type method (EBNUM) via a block unification technique. The accuracy and speed advantages of the EBNUM over the finite difference method (FDM) are established numerically.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Jator, S. (2015) Block Unification Scheme for Elliptic, Telegraph, and Sine-Gordon Partial Differential Equations. American Journal of Computational Mathematics, 5, 175-185. doi: 10.4236/ajcm.2015.52014.

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