The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDF). In this paper, we focus on the derivation of the fourth, sixth and eighth order extended trapezoidal rule of first kind (ETRs) formulae through Hermite polynomial as basis function which we named FETR, SETR and EETR respectively. We then interpolate and collocate at some points of interest to generate the desire method. The stability analysis on our methods suggests that they are not only convergent but possess regions suitable for the solution of stiff ordinary differential equations (ODEs). The methods were very efficient when implemented in block form, they tend to perform better over existing methods.
Published in | American Journal of Mathematical and Computer Modelling (Volume 2, Issue 4) |
DOI | 10.11648/j.ajmcm.20170204.13 |
Page(s) | 103-116 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Stiffness, Hermite Polynomial, ETRs, A-Stability, Ordinary Differential Equations
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APA Style
Yohanna Sani Awari, Micah Geoffrey Kumleng. (2017). Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae. American Journal of Mathematical and Computer Modelling, 2(4), 103-116. https://doi.org/10.11648/j.ajmcm.20170204.13
ACS Style
Yohanna Sani Awari; Micah Geoffrey Kumleng. Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae. Am. J. Math. Comput. Model. 2017, 2(4), 103-116. doi: 10.11648/j.ajmcm.20170204.13
@article{10.11648/j.ajmcm.20170204.13, author = {Yohanna Sani Awari and Micah Geoffrey Kumleng}, title = {Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae}, journal = {American Journal of Mathematical and Computer Modelling}, volume = {2}, number = {4}, pages = {103-116}, doi = {10.11648/j.ajmcm.20170204.13}, url = {https://doi.org/10.11648/j.ajmcm.20170204.13}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20170204.13}, abstract = {The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDF). In this paper, we focus on the derivation of the fourth, sixth and eighth order extended trapezoidal rule of first kind (ETRs) formulae through Hermite polynomial as basis function which we named FETR, SETR and EETR respectively. We then interpolate and collocate at some points of interest to generate the desire method. The stability analysis on our methods suggests that they are not only convergent but possess regions suitable for the solution of stiff ordinary differential equations (ODEs). The methods were very efficient when implemented in block form, they tend to perform better over existing methods.}, year = {2017} }
TY - JOUR T1 - Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae AU - Yohanna Sani Awari AU - Micah Geoffrey Kumleng Y1 - 2017/11/08 PY - 2017 N1 - https://doi.org/10.11648/j.ajmcm.20170204.13 DO - 10.11648/j.ajmcm.20170204.13 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 103 EP - 116 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20170204.13 AB - The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDF). In this paper, we focus on the derivation of the fourth, sixth and eighth order extended trapezoidal rule of first kind (ETRs) formulae through Hermite polynomial as basis function which we named FETR, SETR and EETR respectively. We then interpolate and collocate at some points of interest to generate the desire method. The stability analysis on our methods suggests that they are not only convergent but possess regions suitable for the solution of stiff ordinary differential equations (ODEs). The methods were very efficient when implemented in block form, they tend to perform better over existing methods. VL - 2 IS - 4 ER -