Solving Nonlinear Differential Algebraic Equations by an Implicit GL(n, R) Lie-Group Method

We derive an implicit Lie-group algorithm together with the Newton iterative scheme to solve nonlinear differential algebraic equations. Four numerical examples are given to evaluate the efficiency and accuracy of the new method when comparing the computational results with the closed-form solutions.

[1]  Ander Murua,et al.  Post-projected Runge-Kutta methods for index-2 differential-algebriac equations , 2002 .

[2]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[3]  Chein-Shan Liu.  A Lie-group DSO(n)DSO(n) method for nonlinear dynamical systems , 2013, Appl. Math. Lett..

[4]  Chein-Shan Liu.  Preserving Constraints of Differential Equations by Numerical Methods Based on Integrating Factors , 2006 .

[5]  Chein-Shan Liu,et al.  A method of Lie-symmetry GL(n,R) for solving non-linear dynamical systems , 2013 .

[6]  Jørgen Sand.  On implicit Euler for high-order high-index DAEs , 2002 .

[7]  Carmen Arévalo,et al.  Unitary partitioning in general constraint preserving DAE integrators , 2004, Math. Comput. Model..

[8]  Chein-Shan Liu,et al.  A State Feedback Controller Used to Solve an Ill-posed Linear System by a GL(n, R) Iterative Algorithm , 2013 .

[9]  Esmail Babolian,et al.  System of linear ordinary differential and differential-algebraic equations and pseudo-spectral method , 2010, Comput. Math. Appl..

[10]  Mohammad Mahdi Hosseini.  Adomian decomposition method for solution of nonlinear differential algebraic equations , 2006, Appl. Math. Comput..

[11]  Hong-Ki Hong,et al.  Internal symmetry in the constitutive model of perfect elastoplasticity , 2000 .

[12]  M. Hosseini.  Adomian decomposition method for solution of differential-algebraic equations , 2006 .

[13]  U. Ascher,et al.  Projected implicit Runge-Kutta methods for differential-algebraic equations , 1990 .

[14]  M. Hosseini,et al.  Application of He’s variational iteration method for solution of differential-algebraic equations , 2009 .

[15]  Chein-Shan Liu,et al.  Intermittent transition to quasiperiodicity demonstrated via a circular differential equation , 2000 .

[16]  Chein-Shan Liu.  The steady‐state behavior of the Prandtl‐Reuss material bifurcated under nonproportional circular strain paths , 2003 .