On Approximate Solutions of Second-Order Linear Partial Differential Equations

Yousry S. Hanna

National Research Institute of Astronomy and Geophysics, Helwan, Egypt.

DOI: 10.4236/am.2012.39148                

Abstract

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate value of the unknown Chebyshev coefficients can be found.

Keywords

Chebyshev Polynomial; Differential Equations; Polynomial Approximation

Conflicts of Interest

The authors declare no conflicts of interest.

References

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