A New Self-Adjusting Numerical Integrator for the Numerical Solutions of Ordinary Differential Equations

1
O. O. Enoch
O. O. Enoch
2
Dr. O.O. A. Enoch
Dr. O.O. A. Enoch
3
A.A.Olatunji
A.A.Olatunji
1 Ekiti State University, P.M.B 5363, Ado a Ekiti, Nigeria.

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In this work, we consider a class of formulae for the numerical solution of IVP, in ordinary differential equations with point of singularity, in which the underlying interpolant is a rational function. This is in contrast with the classical formulae which are in general based on polynomial approximation. The proof of convergence and consistency for the scheme are also given. There are two parameters that control the position and the nature of singularity. The values of these parameters are automatically chosen and revised, during the computation.

13 Cites in Articles

References

  1. C Gear (1971). Numerical Initial Value Problems in Ordinary Differential Equations.
  2. S Fatunla (1988). Numerical methods for IVPS.
  3. J Lambert,M Dand Siggurdsson (1972). Multistep Methods with Variables Matrix Coefficients.
  4. J Lambert,I Watson (1976). Symmetric Multistep Methods for Periodic Initial Value Problems.
  5. C Gear (1971). Algorithm 407: DIFSUB for solution of ordinary differential equations [D2].
  6. O Enoch,F Adeyeye (2006). On a new numerical method for the solution of ordinary differential equations.
  7. R Ademiluyi (2005). A 2-Stage Inverse Runge-Kutta Method with Minimum truncation Error for Initial Value Problems of Ordinary Differential EquationIntern.
  8. Simeon Fatunla (1976). A new algorithm for numerical solution of ordinary differential equations.
  9. E Ibijola (1993). On a New fifth-order One-step Algorithm for numerical solution of initial value problem y 1 = f(x, y), y (0) =y 0.
  10. E Ibijola (1998). New Algorithm for Numerical Integration of special initial value problems in ordinary Differential Equations.
  11. E Ibijola,P Kama (1999). On the convergence, consistency and stability of a one-step method for numerical integration of ordinary differential equation.
  12. R Micken (2000). Applications of Nonstandard methods for initial value problems.
  13. Roumen Anguelov,Null- Lubuma (2003). Nonstandard finite difference method by nonlocal approximation.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

O. O. Enoch. 2012. \u201cA New Self-Adjusting Numerical Integrator for the Numerical Solutions of Ordinary Differential Equations\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 12 (GJSFR Volume 12 Issue F11): .

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GJSFR Volume 12 Issue F11
Pg. 25- 35
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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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September 12, 2012

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English

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In this work, we consider a class of formulae for the numerical solution of IVP, in ordinary differential equations with point of singularity, in which the underlying interpolant is a rational function. This is in contrast with the classical formulae which are in general based on polynomial approximation. The proof of convergence and consistency for the scheme are also given. There are two parameters that control the position and the nature of singularity. The values of these parameters are automatically chosen and revised, during the computation.

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A New Self-Adjusting Numerical Integrator for the Numerical Solutions of Ordinary Differential Equations

Dr. O.O. A. Enoch
Dr. O.O. A. Enoch
A.A.Olatunji
A.A.Olatunji

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