Construction of L stable second derivative trigonometrically fitted block backward differentiation formula for the solution of oscillatory initial value problems

2018 ◽  
Vol 10 (4) ◽  
pp. 411-419 ◽  
Author(s):  
R.I. Abdulganiy ◽  
O.A. Akinfenwa ◽  
S.A. Okunuga
Keyword(s):  
Initial Value Problems ◽  
Second Derivative ◽  
Initial Value ◽  
Differentiation Formula ◽  
Backward Differentiation Formula ◽  
Oscillatory Initial Value Problems

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

scholarly journals Construction of Stable High Order One-Block Methods Using Multi-Block Triple

2019 ◽  
pp. 1-13
Author(s):  
I. J. Ajie ◽  
K. Utalor ◽  
M. O. Durojaiye
Keyword(s):  
Initial Value Problems ◽  
Numerical Experiments ◽  
Shift Operator ◽  
Block Method ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
Backward Differentiation Formula ◽  
The Third ◽  
Block Methods

This paper deals with the construction of l-stable implicit one-block methods for the solution of stiff initial value problems. The constructions are done using three different multi-block methods. The first multi-block method is composed using Generalized Backward Differentiation Formula (GBDF) and Backward Differentiation Formula (BDF), the second is composed using Reversed Generalized Adams Moulton (RGAM) and Generalized Adams Moulton (GAM) while the third is composed using Reversed Adams Moulton (RAM) and Adams Moulton (AM). Shift operator is then applied to the combination of the three multi-block methods in such a manner that the resultant block is a one-block method and self-starting. These one-block methods are up to order six and  with at order ten. Numerical experiments show that they are good for solving stiff initial problems.

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

2021 ◽  
Vol 5 (2) ◽  
pp. 120-127
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problems ◽  
Stiff Problems ◽  
Block Method ◽  
Initial Value ◽  
Three Solutions ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Linear And Nonlinear

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 ρ ϵ (-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

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