Journal of Computational and Applied Mathematics
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
The role of orthogonal polynomials in numerical ordinary differential equations
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Analysis of a family of Chebyshev methods for y′′=fx,y
Journal of Computational and Applied Mathematics
Numerical methods for ordinary differential equations in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding
SIAM Journal on Numerical Analysis
A Chebyshev expansion method for solving nonlinear optimal control problems
Applied Mathematics and Computation
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Variable stepsize störmer-cowell methods
Mathematical and Computer Modelling: An International Journal
| Hi-index | 7.29 |
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^'+(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.