The combined Laplace transform and new homotopy perturbation methods for stiff systems of ODEs

Abstract In this paper, we propose new technique for solving stiff system of ordinary differential equations. This algorithm is based on Laplace transform and homotopy perturbation methods. The new technique is applied to solving two mathematical models of stiff problem. We show that the present approach is relatively easy, efficient and highly accurate.

[1]  Livija Cveticanin,et al.  Homotopy–perturbation method for pure nonlinear differential equation , 2006 .

[2]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[3]  Ji-Huan He.  Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[4]  J. Biazar,et al.  A new HPM for ordinary differential equations , 2009 .

[5]  H. Aminikhah.  An analytical approximation for solving nonlinear Blasius equation by NHPM , 2009 .

[6]  A. Yildirim,et al.  He's homotopy perturbation method for solving the shock wave equation , 2009 .

[7]  Numerical methods for extremely stiff systems of ordinary differential equations , 1979 .

[8]  S. Momani,et al.  Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order , 2008 .

[9]  Ernst Hairer,et al.  Rosenbrock-Type Methods , 1996 .

[10]  Hüseyin Koçak,et al.  Homotopy perturbation method for solving the space–time fractional advection–dispersion equation , 2009 .

[11]  H. De Meyer,et al.  Frequency evaluation in exponential fitting multistep algorithms for ODEs , 2002 .

[12]  J. Flaherty,et al.  The numerical solution of boundary value problems for stiff differential equations , 1977 .

[13]  Ji-Huan He,et al.  The homotopy perturbation method for nonlinear oscillators with discontinuities , 2004, Appl. Math. Comput..

[14]  J. Butcher.  Numerical methods for ordinary differential equations , 2003 .

[15]  Jafar Biazar,et al.  Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method , 2007 .

[16]  Ji-Huan He.  HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .

[17]  Hossein Aminikhah,et al.  An efficient method for quadratic Riccati differential equation , 2010 .

[18]  D. Ganji.  The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer , 2006 .