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Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.’s. (English) Zbl 1117.65106
Summary: J. Panovsky and D. L. Richardson [ibid. 23, No. 1, 35–51 (1988; Zbl 0649.65048)] presented a method based on Chebyshev approximations for numerically solving the problem \(y''=f(x, y)\), being the steplength constant. J. P. Coleman and A. S. Booth [ibid. 44, 95–114 (1992; Zbl 0773.65048)] made an analysis 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 [ibid. 158, No. 1, 187–211 (2003; Zbl 1042.65053)], and obtained a scheme for numerically solving the equation \(y''- 2gy'+ (g^2+ w^2)= f(x,y)\). The question of how to extend these formulas to variable stepsize procedures is the primary topic of this paper.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
Full Text: DOI
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