Electron. J. Differential Equations, Vol. 2017 (2017), No. 43, pp. 1-11.

A semi-analytic spectral method for elliptic partial differential equations

Ishtiaq Ali, Maliha Tahseen Saleem

Abstract:
In this article we present a semi-analytic method for solving elliptic partial differential equations. The technique is based on using a spectral method approximation for the second-order derivative in one of the spatial directions followed by solving the resulting system of second-order differential equations by an analytic method. That is, the system of second-order two-point boundary-value problems are solved analytically by casting them in first-order form and solving the resulting set of first-order equations by using the matrix exponential. An important aspect of our technique is that the solution obtained is semi-analytic, e.i., using analytic method in y and spectral method in x. The new method can be used for both linear and non-linear boundary conditions as well as for nonlinear elliptic partial differential equations.

Submitted October 26, 2016. Published February 10, 2017.
Math Subject Classifications: 35J25, 65N35.
Key Words: Semi-analytical technique; Chebyshev-spectral method; exponential matrix.

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Ishtiaq Ali
Department of Mathematics
COMSATS Institute of Information Technology
Park Road, Chak Shahzad, Islamabad 44000, Pakistan
email: ishtiaqali@comsats.edu.pk
  Maliha Tahseen Saleem
Department of Mathematics
COMSATS Institute of Information Technology
Park Road, Chak Shahzad, Islamabad 44000, Pakistan
email: malihasaleem@yahoo.com

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