ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING STIFF INITIAL VALUE PROBLEMS

Authors

Keywords:

A–Stable, Block Method, Enhanced super class of block backward differentiation formula, Super class of block backward differentiation formula, and Zero Stable

Abstract

This paper modified an existing 3–point block method for solving stiff initial value problems.  The modification leads to the derivation of another 3 – point block method which is suitable for solving stiff initial value problems.  The method approximates three solutions values per step and its order is 5. Different sets of formula can be generated from it by varying a parameter Ï Ïµ (-1, 1) in the formula. It has been shown that the method is both Zero stable and A–Stable. Some linear and nonlinear stiff problems are solved and the result shows that the method outperformed an existing method and competes with others in terms of accuracy

Dimensions

Cash, J. R. (1980). On the integration of stiff systems of ODEs using extended backward differentiation formulae. Numerische Mathematik. 34: 235-246.

Cash, J. R. (2000). Modified extended backward differentiation formula for the numerical solution of stoff IVPs in ODE and DAEs." Computational and Applied Mathematics 125, 117-130.

Cheney, E. W.,& Kincaid, D. R. (2012). Numerical mathematics and computing. Brooks/Cole Publishing Company.

Curtiss, C., & Hirschfelder, J.O. (1952). Integration of stiff equations. Proceedings of the National Academy of Sciences of the United States of America, 38, 235-243.

Ibrahim, Z. B., Othman, K.,& Suleiman, M.B. (2007). Implicit r-point block backward differentiation formula for solving first- order stiff ODEs. Applied Mathematics and Computation, 186, 558-565.

Lee, H. C., Chen, C. K., Hung, C. I. (2002). A modified group- preserving scheme for solving the initial value problems of stiff ordinary differential equations. Applied Mathematics and Computation. 133(2-3): 445-459.

Musa, H., Suleiman, M. B., Ismail, F.,Senu, N, Majid and Z. A., Ibrahim, Z. B. (2014). A new fifth order implicit block method for solving first order stiff ordinary differential equations. Malaysian Journal of Mathematicam Sciences 8(S): 45-59.

Musa, H., Bature, B., & Ibrahim, L. K. (2016). Diagonally implicit super class of block backward differentiation formula for solving Stiff IVPs. Journal of the Nigerian Association of Mathematical Physics, 36, 73 – 80.

Suleiman, M. B., Musa, H., Ismail, F., & Senu, N. (2013). A new variable step size block backward differentiation formula for solving stiff IVPs. International Journal of Computer Mathematics. 90 (11), 2391 – 2408.

Suleiman, M. B., Musa, H., Ismail, F., Senu, N. & Ibrahim, Z. B. (2014). A new superclass of block backward differentiation formula for stiff ordinary differential equations. Asian European Journal of Mathematics, 7 (1), 1 – 17.

Vijitha-Kanaka, K. H. (1985). Variable Step size variable order multistep method for stiff ordinary differential equation. Iowa State University.

Zawawi, I. S. M., Ibrahim, Z. B., Ismail, F. and Majid, Z. A. (2012). Diagonally implicit block backward differentiation formula for solving ODEs. International journal of mathematics and mathematical sciences. Article ID 767328.

Published

01-07-2021

How to Cite

ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING STIFF INITIAL VALUE PROBLEMS. (2021). FUDMA JOURNAL OF SCIENCES, 5(2), 120-127. https://doi.org/10.33003/fjs-2021-0501-603

Issue

Vol. 5 No. 2 (2021): FUDMA Journal of Sciences - Vol. 5 No. 2

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING STIFF INITIAL VALUE PROBLEMS. (2021). FUDMA JOURNAL OF SCIENCES, 5(2), 120-127. https://doi.org/10.33003/fjs-2021-0501-603

Most read articles by the same author(s)