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Constructing accurate polynomial approximations for nonlinear differential initial value problems
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DOI：10.1016/j.amc.2007.04.015.png)
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Abstract
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This paper deals with the construction of approximate polynomial solutions, with a prefixed accuracy, of initial value problems for nonlinear ordinary differential equations. By approximating the right-hand side of the equation by an appropriate two-variables Chebyshev polynomial, then applying Frobenius method, and finally truncating this application, an approximate polynomial solution is constructed. Recent results of Chen et al. (2003) [B. Chen, R. Garcia-Bolos, L. Jodar, M.D. Rosello, The truncation error of the two-variable Chebyshev series expansions, Comput. Math. Appl. 45 (2003) 1647-1653] and Chen et al. (2005) [B. Chen, R. Garcia-Bolos, L. Jodar, M.D. Rosello, Chebyshev polynomial approximations for nonlinear differential initial value problems, Nonlinear Anal. 63 (5-7) (2005) e629-e637] are significantly improved in two directions by extending the existence domain of the approximation and by reducing the degree of the truncation polynomial. Several examples are given. (C) 2007 Elsevier Inc. All rights reserved.
Keywords:
polynomial solution
Chebyshev polynomials
error bound
majorant method
initial value problem
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IF:
3.4
Papers:
2.3W
Citations:
3.3W
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