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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.

MSC:
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
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