Open AccessConvergence of the 3-point block backward differentiation formulas with off-step point for stiff ODEs
Author(s) -
Hira Soomro,
Hanita Daud,
Nooraini Zainuddin
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 - 10.1088/1742-6596/1943/1/012137
Subject(s) - ode , consistency (knowledge bases) , mathematics , ordinary differential equation , block (permutation group theory) , convergence (economics) , point (geometry) , backward differentiation formula , differential (mechanical device) , algorithm , differential equation , mathematical analysis , collocation method , geometry , economics , aerospace engineering , economic growth , engineering
Development of 3-Point Block Method with one off-step point using Backward Differentiation Formula (BDF) is presented in this paper to find out the solution for stiff Ordinary Differential Equation (ODEs). By considering the Backward Differentiation Formulas (BBDF), the block method has been derived. It is well known that BBDF is used for solving stiff ODEs. The strategy for the development of this process is to compute three solution values with one off-step point concurrently to each iteration. One off-step point is added in the implicit BBDF method for better accuracy. Derivation of the formulae and consistency properties are generated in this paper. Numerically the proposed method with order five is achieved as a result. Mathematica software has been used for the derivation and consistency of the method.