Enhanced 3-Point Fully Implicit Super Class of Block Backward Differentiation Formula for Solving Stiff Initial Value Problems

Abdullahi, Muhammad; Musa, Hamisu

doi:10.33003/fjs-2021-0501-603

Cited by 3 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In search of accurate scheme, scholars keep developing schemes with good accuracy of the scaled error with executional time. The recent work comprises, Soomro et al [15], Abdullahi et al [16][17][18], Khan et al [19], Shafiq et al [20], Rani et al [21]. Other methods can be found in [23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A New Multi - Block Super Class of BDF for Integrating First Order Stiff IVP of ODEs

Abdullahi¹,

Danbaba²,

Abdulseed³

2023

Curr. Res. Interdiscip. Stud.

View full text Add to dashboard Cite

A new multi-block super class of backward differentiation formula for integrating first order stiff IVPs with a variable mesh size strategy is derived. The proposed scheme approximate two solution values at a time per integration step. The stability properties are achieved by varying the mesh size ratio in the formula to generate more zero stable and A-Stable schemes, capable of solving stiff IVPs of ODEs. Approximates result from the system of stiff ODE problems considered are found to favorably validate the new method in terms of accuracy of the scale error and less executional time in respect to the two methods compared in the study. Hence, the proposed scheme can be used for solving for stiff IVPs of ODEs.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Put ℎ = ℎʎ in(15)(16)(17), we have Set ℎ = ℎʎ = 0 in(15)(16)(17) and solve for 𝑡 in all the polynomials. The following table is obtained with the respective roots of the polynomials 𝑡…”

mentioning

confidence: 99%

A New Multi - Block Super Class of BDF for Integrating First Order Stiff IVP of ODEs

Abdullahi¹,

Danbaba²,

Abdulseed³

2023

Curr. Res. Interdiscip. Stud.

View full text Add to dashboard Cite

show abstract

Maple Simulation Codes for Stability Analysis of Variable Step Super Class of Block Backward Differentiation Formula for Integrating a System of First Order Stiff Ivps

Abdullahi,

Bello,

Danbaba

2023

FJS

Self Cite

View full text Add to dashboard Cite

Strength of numerical scheme is rated by the properties it possessed and in turn the kind of problems it can handle. Zero stable method can effectively handle ODEs problem. While, an A – stable method can solve stiff ODEs problem. Analyzing stability of block methods are been carried out using various software. This work aimed at using simplified Maple simulation code to critically analyze avariable step size multi-block backward differentiation formula for the solution stiff initial value problems of ordinary differential equations. The Graphical comparisons of the simulated result obtained is made using Matlab to depict the performing schemes.

show abstract

Convergence Test for the Extended 3 - Point Super Class of Block Backward Differentiation Formula for Integrating Stiff Ivp

Bello,

Danbaba,

Garba

2023

FJS

View full text Add to dashboard Cite

In this work, a new scheme is generated from the extended 3–point super class of block backward differentiation formula for integrating stiff IVP and the proposed method is subjected to convergence test. The proposed scheme is found to be zero stable, consistent and of order 5. Thus, possess all the required criteria for convergence. The scheme can approximate the values of three points at a time per integration step. The scheme maintained the same technique of co-opting a stability control parameter () in the formula and by adjusting its value within the interval , more A-stabled schemes can be generated. However, this research considers and arrived at zero and A– Stabled method, capable of solving any stiff IVPs. Hence, the proposed convergent scheme can be used for integrating stiff IVPs and archives accuracy of scale error and less executional time.

show abstract

Enhanced 3-Point Fully Implicit Super Class of Block Backward Differentiation Formula for Solving Stiff Initial Value Problems

Cited by 3 publications

References 6 publications

A New Multi - Block Super Class of BDF for Integrating First Order Stiff IVP of ODEs

A New Multi - Block Super Class of BDF for Integrating First Order Stiff IVP of ODEs

Maple Simulation Codes for Stability Analysis of Variable Step Super Class of Block Backward Differentiation Formula for Integrating a System of First Order Stiff Ivps

Convergence Test for the Extended 3 - Point Super Class of Block Backward Differentiation Formula for Integrating Stiff Ivp

Contact Info

Product

Resources

About