Open AccessModified higher order block backward differentiation formula for third order ordinary differential equations
Author(s) -
Asma Izzati Asnor,
Siti Ainor Mohd Yatim,
Zulkifilie Ibrahim
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1988/1/012004
Subject(s) - ode , ordinary differential equation , backward differentiation formula , mathematics , block (permutation group theory) , l stability , solver , third order , order (exchange) , differential (mechanical device) , reduction of order , differential equation , runge–kutta methods , mathematical optimization , mathematical analysis , differential algebraic equation , geometry , engineering , law , finance , aerospace engineering , political science , economics
This study is aimed to modify higher order block backward differentiation formulae for dealing with the third order stiff ordinary differential equations (ODEs). Two new solutions are acquired at each step by using a few back values in preceding blocks. Apart from that, the differentiation coefficients will be stored, thus, repetitive calculations of the coefficients can be avoided as well as computational cost can also be optimized. A comparative analysis will be presented once the numerical experiments have been conducted to a few considered problems in order to confirm the efficiency of the proposed method with the existing stiff ODE solver. The analysis proves the accuracy and efficiency of the proposed method can be served as another alternative for third order stiff ODEs.