The Simulation of One-Step Algorithms for Treating Higher Order Initial Value Problems
J. Sabo, A. M. Ayinde, A. A. Ishaq, G. Ajileye
Asian Research Journal of Mathematics · pp. 34–47 · Published 6 Nov 2021
10.9734/arjom/2021/v17i930329Abstract
The simulation of one-step methods using interpolation and collocation for the treatment of higher order initial value problems is proposed in this paper. The new approach is derived using interpolation and collocation as a basic function through power series polynomial, where the basic properties are also analyzed. The derived method is used to treat some highly stiff linear problems. The new approach compute clearly showed that the method is reliable, efficient and gives faster convergence when compared with those in literature.
References (17)
- 1 Computational methods in ordinary differential equations [DOI]
- 2 Convergence and stability in the numerical integration of ordinary differential equations [DOI]
- 3 A class of continuous methods for general second order initial value problems in ordinary differential equations [DOI]
- 4 A Five-Step P-Stable Method for the Numerical Integration of Third Order Ordinary Differential Equations [DOI]
- 5 A Subdivision Based Iterative Collocation Algorithm for Nonlinear Third-Order Boundary Value Problems [DOI]
- 6 Numerical solution of third order ordinary differential equations using a seven-step block method [DOI]
- 7 Stability of Adams-Type Formulae for Second-Order Ordinary Differential Equations [DOI]
- 8 A New Integrator for Special Third Order Differential Equations With Application to Thin Film Flow Problem [DOI]
- 9 New algorithms for the continuous approximate solutions of ordinary differential equations and the upgrading of the order of the processes [DOI]
- 10 Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations [DOI]
- 11 Predictor-corrector block method of order seven for solving third order ordinary differential equations [DOI]
- 12 Numerical Treatment of General Third Order Ordinary Differential Equations Using Taylor Series as Predictor [DOI]
- 13 New self-starting approach for solving special third order initial value problems
- 14 Developing Parallel 3-Point Implicit block Method For Solving Second order Ordinary Differential equations Directly [DOI]
- 15 Numerical application of third derivative hybrid block methods on third order initial value problem of ordinary differential equations
- 16 The Direct Simulation of Third Order Linear Problems on Single Step Block Method [DOI]
- 17 Numerical methods for initial value problems in ordinary differential equations [DOI]
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