A semi-analytic spectral method for elliptic partial differential equations




Ali, Ishtiaq
Saleem, Maliha Tahseen

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Texas State University, Department of Mathematics


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.



Semi-analytical technique, Chebyshev-spectral method, Exponential matrix


Ali, I., & Saleem, M. T. (2017). A semi-analytic spectral method for elliptic partial differential equations. <i>Electronic Journal of Differential Equations, 2017</i>(43), pp. 1-11.


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