A variational iteration method for solving Troesch's problem

Troesch's problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch's problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity in the problem into polynomial-type nonlinearities by variable transformation, and the variational iteration method is then directly used to solve this transformed problem. Only the second-order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods.

[1]  D. Gidaspow,et al.  A Model for Discharge of Storage Batteries , 1973 .

[2]  Shih-Hsiang Chang,et al.  A new algorithm for calculating two-dimensional differential transform of nonlinear functions , 2009, Appl. Math. Comput..

[4]  Liquan Mei,et al.  An efficient algorithm for solving Troesch's problem , 2007, Appl. Math. Comput..

[5]  Y. Vasil’ev,et al.  Fuel cells : their electrochemical kinetics , 1966 .

[6]  Shaher Momani,et al.  Variational iteration method for solving nonlinear boundary value problems , 2006, Appl. Math. Comput..

[7]  V. Vemuri,et al.  On a Method of Solving Sensitive Boundary Value Problems , 1979 .

[8]  Tsung-Yen Na,et al.  On the solution of Troesch's nonlinear two-point boundary value problem using an initial value method , 1975 .

[9]  H. Bowen,et al.  Osmotic pressure for concentrated suspensions of polydisperse particles with thick double layers , 1987 .

[10]  E. S. Weibel.  On the Confinement of a Plasma by Magnetostatic Fields , 1959 .

[11]  Angelo Miele,et al.  Solution of Two-Point Boundary-Value Problems with Jacobian Matrix Characterized by Large Positive Eigenvalues , 1974 .

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

[13]  S. M Roberts,et al.  Solution of Troesch's two-point boundary value problem by a combination of techniques , 1972 .

[14]  D. J Jones.  Solution of Troesch's, and other, two point boundary value problems by shooting techniques , 1973 .

[15]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[16]  B. A Troesch,et al.  A simple approach to a sensitive two-point boundary value problem , 1976 .

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

[18]  Shih-Hsiang Chang.  Numerical solution of Troesch's problem by simple shooting method , 2010, Appl. Math. Comput..

[19]  Melvin R. Scott,et al.  ON THE CONVERSION OF BOUNDARY-VALUE PROBLEMS INTO STABLE INITIAL-VALUE PROBLEMS VIA SEVERAL INVARIANT IMBEDDING ALGORITHMS , 1975 .

[20]  S. Khuri,et al.  An Algorithm for Solving Boundary Value Problems , 2000 .

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

[22]  S. M. Roberts,et al.  On the closed form solution of Troesch's problem , 1976 .

[23]  Vladimir Hlavacek,et al.  Solution of Troesch's two-point boundary value problem by shooting technique , 1975 .

[24]  J. A. Snyman.  Continuous and discontinuous numerical solutions to the Troesch problem , 1979 .

[25]  S. A. Khuri.  A Numerical Algorithm For Solving Troesch'S Problem , 2003, Int. J. Comput. Math..