Derivation of the Adomian decomposition method using the homotopy analysis method. (English) Zbl 1125.65063
The solution of a nonlinear equation \( L(y(x)) + N(y(x)) = 0 \), where \(L\) and \(N\) are linear and nonlinear operators, respectively, is represented in the form
\[ y =\sum_{n=0}^{\infty} y_{n} . \] The terms \(y_{n}\) can be calculated by recurrent relations using the decomposition \[ N(y)=\sum_{n=0}^{\infty} A_{n}, \] where \(A_{n}\) are the Adomian polynomials. The author proves that this method can be obtained using another analytical method.
\[ y =\sum_{n=0}^{\infty} y_{n} . \] The terms \(y_{n}\) can be calculated by recurrent relations using the decomposition \[ N(y)=\sum_{n=0}^{\infty} A_{n}, \] where \(A_{n}\) are the Adomian polynomials. The author proves that this method can be obtained using another analytical method.
Reviewer: Ivan Secrieru (Chişinău)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34L30 | Nonlinear ordinary differential operators |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
nonlinear differential equation; analytical solution; method of decomposition in series; error analysis; convergence criteriaReferences:
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