Chebyshev collocation method for solving second order ODEs using integration matrices
Journal: Discrete and Continuous Models and Applied Computational Science (Vol.31, No. 2)Publication Date: 2023-06-30
Authors : Konstantin Lovetskiy; Dmitry Kulyabov; Leonid Sevastianov; Stepan Sergeev;
Page : 150-163
Keywords : ordinary differential equation; spectral methods; two-point boundary value problems;
Abstract
The spectral collocation method for solving two-point boundary value problems for second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. The approach allows a stable calculation of both the spectral representation of the solution and its pointwise representation on any required grid in the definition domain of the equation and additional conditions of the multipoint problem. For the effective construction of SLAE, the solution of which gives the desired coefficients, the Chebyshev matrices of spectral integration are actively used. The proposed algorithms have a high accuracy for moderate-dimension systems of linear algebraic equations. The matrix of the system remains well-conditioned and, with an increase in the number of collocation points, allows finding solutions with ever-increasing accuracy.
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Last modified: 2023-07-03 05:47:00