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2014•Universiti Putra Malaysia Institutional Repository (Universiti Putra Malaysia)Open access

A New Fifth Order Implicit Block Method for Solving First Order Stiff Ordinary Differential Equations

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

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Abstract

A new implicit block backward differentiation formula that computes 3–points simultaneously is derived. The method is of order 5 and solves system of stiff ordinary differential equations (ODEs). The stability analysis indicates that the method is A–stable. Numerical results show that the method outperformed some existing block and non-block methodsfor solving stiff ODEs.

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A new implicit block backward differentiation formula that computes 3–points simultaneously is derived. The method is of order 5 and solves system of stiff ordinary differential equations (ODEs). The stability analysis indicates that the method is A–stable. Numerical results show that the method outperformed some existing block and non-block methodsfor solving stiff ODEs.

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Available abstract

A new implicit block backward differentiation formula that computes 3–points simultaneously is derived. The method is of order 5 and solves system of stiff ordinary differential equations (ODEs). The stability analysis indicates that the method is A–stable. Numerical results show that the method outperformed some existing block and non-block methodsfor solving stiff ODEs.

Key concepts: L-stability, Ordinary differential equation, Backward differentiation formula, Mathematics, Explicit and implicit methods, Ode, Block (permutation group theory), Numerical methods for ordinary differential equations

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