Analysis of non-linear singular system from fluid dynamics using extended runge-kutta methods

A non-linear singular system from fluid dynamics has been analysed by considering various possibilities using three different fourth order extended Runge–Kutta (RK) methods based on arithmetic mean, harmonic mean and heronian mean. It is observed that the extended RK methods suit well for the nuclear reactor core problem, when compared to the Single Term Walsh Series (STWS) method [1,10]. The simple and direct methods presented here can easily be implemented in a digital computer.

[1]  K. Murugesan,et al.  Numerical solution of a singular nonlinear system from fluid dynamics , 1991, Int. J. Comput. Math..

[2]  K. R. Palanisamy,et al.  Analysis of smoothing circuits using a single-term Walsh series , 1985 .

[3]  T. Srinivasan,et al.  Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems , 1980 .

[4]  Stephen L. Campbell,et al.  On using orthogonal functions with singular systems , 1984 .

[5]  On using orthogonal functions for the analysis of singular systems , 1985 .

[6]  K. Balachandran,et al.  Analysis of different systems via single-term walsh series method , 1990 .

[7]  K. R. Palanisamy,et al.  Analysis of non-linear systems via single term Walsh series approach , 1982 .

[8]  Krishnan Balachandran,et al.  Single-term Walsh series approach to singular systems , 1987 .

[9]  V. P. Arunachalam,et al.  Analysis of bilinear systems via single-term Walsh series , 1985 .

[10]  K. Balachandran,et al.  Analysis of electronic circuits using the single-term Walsh series approach , 1990 .

[11]  David J. Evans,et al.  Analysis of different second order systems via runge-kutta method , 1999, Int. J. Comput. Math..

[12]  R. Alexander,et al.  Runge-Kutta methods and differential-algebraic systems , 1990 .

[13]  D. J. Evans,et al.  A new fourth order runge-kutta formula based on the harmonic mean , 1994 .

[14]  C. F. Chen,et al.  A state-space approach to Walsh series solution of linear systems , 1975 .

[15]  Michel Roche,et al.  Implicit Runge-Kutta methods for differential algebraic equations , 1989 .

[16]  David J. Evans,et al.  A fourth order runge-kutta method based on the heronian mean formula , 1995, Int. J. Comput. Math..