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2018•African Journal of Mathematics and Computer Science ResearchRequires access

Derivation of a new block fifth order method for numerical solution of first order initial value problems

Salman Abbas, Noor A. Jalil Alshakhoori

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Abstract

A new block method of order five for the numerical solution of initial value problems is derived. The coefficients of the matrix of the method are chosen such that low power of the blocksize appears in the principal local truncation error. The stability polynomial is shown to be a perturbation of   order explicit Runge-Kutta method. Key words: Predictor-corrector methods, ordinary differential equations, block methods.

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What this paper is about

A new block method of order five for the numerical solution of initial value problems is derived. The coefficients of the matrix of the method are chosen such that low power of the blocksize appears in the principal local truncation error. The stability polynomial is shown to be a perturbation of   order explicit Runge-Kutta method. Key words: Predictor-corrector methods, ordinary differential equations, block methods.

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Available abstract

A new block method of order five for the numerical solution of initial value problems is derived. The coefficients of the matrix of the method are chosen such that low power of the blocksize appears in the principal local truncation error. The stability polynomial is shown to be a perturbation of   order explicit Runge-Kutta method. Key words: Predictor-corrector methods, ordinary differential equations, block methods.

Key concepts: Mathematics, Runge–Kutta methods, Applied mathematics, Ordinary differential equation, L-stability, Reduction of order, Initial value problem, Block (permutation group theory)

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