A NEW 2-POINT DIAGONALLY IMPLICIT VARIABLE STEP SIZE SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER STIFF INITIAL VALUE PROBLEMS

Authors

  • Bala Najamuddeen
    Federal Polytechnic Kaura Namoda
  • Musa Hamisu
    Umaru Musa Yar’adua University, Katsina
  • Sani Abba
    Umaru Musa Yar’adua University, Katsina

Keywords:

Diagonally implicit block method, Variable step size, Stiff, Order, Zero stability, Blocks backward differentiation formula, A–Stability

Abstract

A new 2-point diagonally implicit variable step size super class of block backward differentiation formula (2DVSSBBDF) for solving first order stiff initial value problems (IVPs) is developed. The method is derived by introducing a lower triangular matrix in the coefficient matrix of existing 2-point variable step size superclass of block backward differentiation formula for the integration of stiff IVPs. The order of the method is 4. The stability analysis indicates that the method is both zero and A-stable.  The Numerical results obtained are compared with some existing built in Matlab ODEs solvers in particular ODE15s and ODE23s and the performance of the new scheme showed an advantage in accuracy and computation time over some existing algorithms. The new method can serve as an alternative and efficient method for solving stiff IVPs.

Dimensions

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Published

22-07-2025

How to Cite

A NEW 2-POINT DIAGONALLY IMPLICIT VARIABLE STEP SIZE SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER STIFF INITIAL VALUE PROBLEMS. (2025). FUDMA JOURNAL OF SCIENCES, 9(7), 275-282. https://doi.org/10.33003/fjs-2025-0907-3799

Issue

Vol. 9 No. 7 (2025): FUDMA Journal of Sciences - Vol. 9 No. 7

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

A NEW 2-POINT DIAGONALLY IMPLICIT VARIABLE STEP SIZE SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER STIFF INITIAL VALUE PROBLEMS. (2025). FUDMA JOURNAL OF SCIENCES, 9(7), 275-282. https://doi.org/10.33003/fjs-2025-0907-3799