Open AccessBBDF-Alpha for solving stiff ordinary differential equations with oscillating solutions
Author(s) -
Iskandar Shah Mohd Zawawi
Publication year - 2020
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.51.2020.2964
Subject(s) - mathematics , ordinary differential equation , convergence (economics) , stability (learning theory) , consistency (knowledge bases) , alpha (finance) , mathematical analysis , block (permutation group theory) , plane (geometry) , backward differentiation formula , differential equation , differential algebraic equation , geometry , internal consistency , computer science , statistics , machine learning , economics , economic growth , psychometrics
In this paper, the block backward differentiation α formulas (BBDF-α) is derived for solving first order stiff ordinary differential equations with oscillating solutions. The consistency and zero stability conditions are investigated to prove the convergence of the method. The stability region in the entire negative half plane shows that the derived method is A-stable for certain values of α. The implementation of the method using Newton iteration is also discussed. Several numerical experiments are conducted to demonstrate the performance of the method in terms of accuracy and computational time.