Abstract
This paper will present the two-point block one-step method for solving stiff ordinary differential equations (ODE s). The propose block method is A-stable and the order is three. The solutions will be obtain simultaneously in block and produces two approximate solutions using constant step size. The method is similar as the one-step method and it is self-starting but the im- plementation is based on the predictor and corrector formulae. The order of the method will be discussed. The numerical results is presented to illustrate the applicability of the propose method. The results clearly shown that the propose method is able to produce comparable and better results compared to the existing method when solving stiff differential equations.
Highlights
Stiff equation in mathematics is a differential equation that may gives unstable result if it is solve using certain numerical method, unless the step size takenReceived: February 5, 2014 §Correspondence author c 2014 Academic Publications, Ltd. url: www.acadpubl.euM.Z.M
Sharmila et al [10] had developed a new third order weight Runge-Kutta formula based on Centoridal Mean (CeM) for solving stiff equation
In 2003, Majid et al.[15] has improved this method by proposed a block method by integrating using the closest point in the interval based on Newton backward divided difference formula but the author has solved the non stiff ODEs where the implementation only used the fixed iteration or known as simple iteration
Summary
Stiff equation in mathematics is a differential equation that may gives unstable result if it is solve using certain numerical method, unless the step size taken. Sharmila et al [10] had developed a new third order weight Runge-Kutta formula based on Centoridal Mean (CeM) for solving stiff equation. Nasir et al [6] had developed a two-point implicit code in the form of fifth order block backward differential formula (BBDF5) for solving first order stiff ODEs using constant step size. In 2003, Majid et al.[15] has improved this method by proposed a block method by integrating using the closest point in the interval based on Newton backward divided difference formula but the author has solved the non stiff ODEs where the implementation only used the fixed iteration or known as simple iteration. We propose the two-point block one-step method in Majid et al.[15] with Newton’s iteration for solving stiff differential equation.
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