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 |
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| 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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