scholarly journals Corrigendum to “Derivation of Diagonally Implicit Block Backward Differentiation Formulas for Solving Stiff Initial Value Problems”

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Iskandar Shah Mohd Zawawi ◽  
Zarina Bibi Ibrahim ◽  
Khairil Iskandar Othman
Keyword(s):  
Initial Value Problems ◽  
Initial Value ◽  
Stiff Initial Value Problems ◽  
Backward Differentiation Formulas ◽  
Differentiation Formulas

scholarly journals Derivation of Diagonally Implicit Block Backward Differentiation Formulas for Solving Stiff Initial Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Iskandar Shah Mohd Zawawi ◽  
Zarina Bibi Ibrahim ◽  
Khairil Iskandar Othman
Keyword(s):  
Initial Value Problems ◽  
Maximum Error ◽  
Computational Time ◽  
Initial Value ◽  
Stiff Initial Value Problems ◽  
Fully Implicit ◽  
Backward Differentiation Formulas ◽  
The Stability ◽  
Order Four ◽  
Differentiation Formulas

The diagonally implicit 2-point block backward differentiation formulas (DI2BBDF) of order two, order three, and order four are derived for solving stiff initial value problems (IVPs). The stability properties of the derived methods are investigated. The implementation of the method using Newton iteration is also discussed. The performance of the proposed methods in terms of maximum error and computational time is compared with the fully implicit block backward differentiation formulas (FIBBDF) and fully implicit block extended backward differentiation formulas (FIBEBDF). The numerical results show that the proposed method outperformed both existing methods.

scholarly journals A Family of High Order One-Block Methods for the Solution of Stiff Initial Value Problems

2019 ◽  
pp. 1-14
Author(s):  
I. J. Ajie ◽  
K. Utalor ◽  
P. Onumanyi
Keyword(s):  
Numerical Methods ◽  
Initial Value Problems ◽  
High Order ◽  
Numerical Implementation ◽  
Initial Value ◽  
Stiff Initial Value Problems ◽  
The Family ◽  
Block Methods ◽  
Backward Differentiation Formulas ◽  
Differentiation Formulas

In this paper, we construct a family of high order self-starting one-block numerical methods for the solution of stiff initial value problems (IVP) in ordinary differential equations (ODE). The Reversed Adams Moulton (RAM) methods, Generalized Backward Differentiation Formulas (GBDF) and Backward Differentiation Formulas (BDF) are used in the constructions. The E-transformation is applied to the triples and a family of self-starting methods are obtained. The family is for . The numerical implementation of the methods on some stiff initial value problems are reported to show the effectiveness of the methods. The computational rate of convergence tends to the theoretical order as h tends to zero.

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 Block Backward Differentiation Formulas for Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
T. A. Biala ◽  
S. N. Jator
Keyword(s):  
Numerical Approximation ◽  
Initial Value ◽  
One Dimensional ◽  
Numerical Tests ◽  
Numerical Integrators ◽  
Backward Differentiation Formulas ◽  
Collocation Approach ◽  
Fractional Differential ◽  
Large Systems ◽  
Differentiation Formulas

This paper concerns the numerical approximation of Fractional Initial Value Problems (FIVPs). This is achieved by constructing k-step continuous BDFs. These continuous schemes are developed via the interpolation and collocation approach and are used to obtain the discrete k-step BDF and (k-1) additional methods which are applied as numerical integrators in a block-by-block mode for the integration of FIVP. The properties of the methods are established and regions of absolute stability of the methods are plotted in the complex plane. Numerical tests including large systems arising form the semidiscretization of one-dimensional fractional Burger’s equation show that the methods are highly accurate and efficient.

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