The solution of nonlinear coagulation problem with mass loss

The coagulation problem, which is an important process in many different scientific fields, is described as a nonlinear problem. Through this work, the nonlinear coagulation problem with linear continuous mass loss is solved using two different techniques, the Adomian’s decomposition method and the He’s variational-iteration method. The solution of the problem is carried-out for two different kernels and different initial conditions. The calculations are carried out for different values of the mass loss coefficient. He’s variational-iteration method is easier than the Adomian’s decomposition method and it is introduced to overcome the difficulty arising in calculating Adomian’s polynomials.

[1]  Ji-Huan He.  A new approach to nonlinear partial differential equations , 1997 .

[2]  G. J. Rodgers,et al.  Coagulation processes with mass loss , 1996 .

[3]  Abdul-Majid Wazwaz,et al.  A reliable modification of Adomian decomposition method , 1999, Appl. Math. Comput..

[4]  Harvey Gould,et al.  Kinetics of Aggregation and Gelation , 1985 .

[5]  Shaher Momani,et al.  Application of He’s variational iteration method to Helmholtz equation , 2006 .

[6]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[7]  G. Adomian.  A new approach to nonlinear partial differential equations , 1984 .

[8]  S. Friedlander,et al.  Smoke, dust, and haze , 2000 .

[9]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[10]  B. Finlayson.  The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[11]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[12]  Abdul-Majid Wazwaz,et al.  A new algorithm for calculating adomian polynomials for nonlinear operators , 2000, Appl. Math. Comput..

[13]  H. Aref,et al.  Self-similarity theory of stationary coagulation , 2002 .

[14]  Jianhong Wu,et al.  Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation , 2000, Appl. Math. Comput..

[15]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[16]  Ji-Huan He.  Approximate solution of nonlinear differential equations with convolution product nonlinearities , 1998 .

[17]  H. Sekine,et al.  General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics1 , 1980 .

[18]  G. Adomian.  A review of the decomposition method in applied mathematics , 1988 .

[19]  Ji-Huan He,et al.  An iteration formulation for normalized diode characteristics , 2004, Int. J. Circuit Theory Appl..

[20]  A. Wazwaz.  A new approach to the nonlinear advection problem: an application of the decomposition method , 1995 .

[21]  Ji-Huan He.  Approximate analytical solution for seepage flow with fractional derivatives in porous media , 1998 .