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A collocation approach for solving linear complex differential equations in rectangular domains
Author(s) -
Yüzbaşi Şuayip,
Şahin Niyazi,
Sezer Mehmet
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1590
Subject(s) - mathematics , orthogonal collocation , collocation method , bessel function , collocation (remote sensing) , domain (mathematical analysis) , differential equation , mathematical analysis , matrix (chemical analysis) , complex differential equation , linear differential equation , numerical analysis , computation , algorithm , computer science , ordinary differential equation , materials science , machine learning , composite material
In this paper, a collocation method is presented to find the approximate solution of high‐order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a). Copyright © 2012 John Wiley & Sons, Ltd.