This paper investigates two basic steps of the homotopy analysis method (HAM) when applied to nonlinear boundary value problems of the chemical reaction kinetics, namely (1) the prediction and (2) the effective calculation of multiple solutions. To be specific, the approach is applied to the dual so
Simplicial homotopy method for the solution of nonlinear two-point boundary value problems
β Scribed by Kiyotaka Yamamura; Shin'Ichi Oishi; Kazuo Horiuchi
- Book ID
- 112075318
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 707 KB
- Volume
- 68
- Category
- Article
- ISSN
- 8756-6621
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We study a new nonlinear shooting method for solving two-point boundary value problems and show numerical experiments with various initial velocity conditions. We discuss and analyze the numerical solutions which are obtained by the shooting method.
## Communicated by J. Cash 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 c
By in proper transformation, a class of strongly nonlinear two-point boundary value problems are transformed into semilinear problems so that the well-known Numerov's method can be applied. Some applications and numerical results are presented to demonstrate the efficiency of the approach.