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VARIABLE STEP BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER STIFF ODEs

Zarina Bibi İbrahim, Khairil Iskandar Othman, Mohamed Suleiman

Open publisher page 19 citations

Abstract

Abstract — This paper focuses on the derivation of implicit 2-point block method based on Backward Differentiation Formulae (BDF) of variable step size for solving first order stiff initial value problems (IVPs) for Ordinary Differential Equations (ODEs). In a 2-point Block Backward Differentiation Formula (BBDF), two solution values are produced simultaneously. Plots of their regions of absolute stability for the method are also presented. The efficiency of the 2-point BBDF is compared with variable step variable order non block BDF (NBDF) method. Numerical results indicate that the resulting 2-point BBDF method outperform the NBDF method in both execution time and accuracy.

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What this paper is about

Abstract — This paper focuses on the derivation of implicit 2-point block method based on Backward Differentiation Formulae (BDF) of variable step size for solving first order stiff initial value problems (IVPs) for Ordinary Differential Equations (ODEs). In a 2-point Block Backward Differentiation Formula (BBDF), two solution values are produced simultaneously. Plots of their regions of absolute stability for the method are also presented. The efficiency of the 2-point BBDF is compared with variable step variable order non block BDF (NBDF) method. Numerical results indicate that the resulting 2-point BBDF method outperform the NBDF method in both execution time and accuracy.

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Available abstract

Abstract — This paper focuses on the derivation of implicit 2-point block method based on Backward Differentiation Formulae (BDF) of variable step size for solving first order stiff initial value problems (IVPs) for Ordinary Differential Equations (ODEs). In a 2-point Block Backward Differentiation Formula (BBDF), two solution values are produced simultaneously. Plots of their regions of absolute stability for the method are also presented. The efficiency of the 2-point BBDF is compared with variable step variable order non block BDF (NBDF) method. Numerical results indicate that the resulting 2-point BBDF method outperform the NBDF method in both execution time and accuracy.

Key concepts: Ode, Ordinary differential equation, Variable (mathematics), Mathematics, Block (permutation group theory), Initial value problem, Backward differentiation formula, Stability (learning theory)

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VARIABLE STEP BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER STIFF ODEs — Research Paper | ScholarLens