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An improved 2–point block backward differentiation formula for solving stiff initial value problems

Hamisu Musa, Mohamed Bin Suleiman, Fudziah Ismail, Norazak Senu, Zarina Bibi İbrahim

Open publisher page 18 citations

Abstract

A new block method that generates two values simultaneously is developed for the integration of stiff initial value problems. The method is proven to be A – stable and is a super class of the 2 – point block backward differentiation formula (BBDF). A comparison is made between the method, 1 point backward differentiation formula (BDF) and the 2 point BBDF methods. The numerical results indicate that the new method outperformed the 1 point BDF and the 2 point BBDF methods in terms of accuracy and stability. The total number of steps to complete the integration by the 1 point BDF method is reduced to half. Computation time for the method is also competitive.

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What this paper is about

A new block method that generates two values simultaneously is developed for the integration of stiff initial value problems. The method is proven to be A – stable and is a super class of the 2 – point block backward differentiation formula (BBDF). A comparison is made between the method, 1 point backward differentiation formula (BDF) and the 2 point BBDF methods. The numerical results indicate that the new method outperformed the 1 point BDF and the 2 point BBDF methods in terms of accuracy and stability. The total number of steps to complete the integration by the 1 point BDF method is reduced to half. Computation time for the method is also competitive.

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OpenAlex reports 18 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A new block method that generates two values simultaneously is developed for the integration of stiff initial value problems. The method is proven to be A – stable and is a super class of the 2 – point block backward differentiation formula (BBDF). A comparison is made between the method, 1 point backward differentiation formula (BDF) and the 2 point BBDF methods. The numerical results indicate that the new method outperformed the 1 point BDF and the 2 point BBDF methods in terms of accuracy and stability. The total number of steps to complete the integration by the 1 point BDF method is reduced to half. Computation time for the method is also competitive.

Key concepts: Block (permutation group theory), Mathematics, Computation, Point (geometry), Stability (learning theory), Algorithm, Value (mathematics), Numerical integration

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