An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method

作者：Hassan Hany N^*; El Tawil Magdy A

来源：Mathematical Methods in the Applied Sciences, 2011, 34(8): 977-989.

DOI：10.1002/mma.1416

• homotopy analysis method
• two point nonlinear boundary value problems
• convergence-controller parameter
• Taylor expansion
• Troesch's problem
• Bratu's equation

In this paper, we use homotopy analysis method (HAM) to solve two-point nonlinear boundary value problems that have at least one solution. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The scheme shows importance of choice of convergence-control parameter h to guarantee the convergence of the solutions of nonlinear differential equations. This scheme is tested on three nonlinear exactly solvable differential equations. Two of the examples are practical in science and engineering. The results demonstrate reliability, simplicity and efficiency of the algorithm developed.

• 出版日期2011-5-30