Malaysian Journal of Mathematical Sciences, September 2019, Vol. 13, No. 3
An Explicit Time-Stepping Method Based on Error Minimization for Solving Stiff System of Ordinary Differential Equations
Rahmanzadeh, M. and Barfeie, M.
Corresponding Email: rahmanzadeh.mostafa@gmail.com
Received date: 20 October 2017
Accepted date: 29 May 2019
Abstract:
In this paper, an explicit one step method is presented for numerical solution of stiff systems of ordinary differential equations (ODEs). In this
method, the solution of the ODE is considered as a polynomial. The numerical approximation is obtained by minimizing an error function that is defined based on residual error. The stability region of the proposed method is obtained. In contrast to Runge-Kutta (RK) method that use Taylor polynomial, the method has larger stability region and a larger stable step size can be selected to obtain the numerical solutions. Numerical experiments show that the method is more accurate than explicit and implicit methods such as implicit Runge-Kutta Methods (IRK) of order eighth.
Keywords: Ordinary Differential Equations, Stability Region, Runge-Kutta Method, Stiff System, Explicit Method
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