Variable-stepsize Chebyshev-type methods for the integration of second-order IVP's

Autores: Higinio Ramos Calle , Jesús Vigo-Aguiar
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 204, Nº 1, 2007, págs. 102-113
Idioma: inglés
DOI: 10.1016/j.cam.2006.04.032
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Resumen
- Panovsky and Richardson [A family of implicit Chebyshev methods for the numerical integration of second-order differential equations, J. Comput. Appl. Math. 23 (1988) 35�51] presented a method based on Chebyshev approximations for numerically solving the problem y?=f(x,y), being the steplength constant. Coleman and Booth [Analysis of a Family of Chebyshev Methods for y?=f(x,y), J. Comput. Appl. Math. 44 (1992) 95�114] made an analysis of the above method and suggested the convenience to design a variable steplength implementation. As far as we know this goal has not been achieved until now. Later on we extended the above method (this journal, 2003), and obtained a scheme for numerically solving the equation y?-2gy'+(g2+w2)=f(x,y). The question of how to extend these formulas to variable stepsize procedures is the primary topic of this paper.