期刊
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
卷 32, 期 11, 页码 3470-3483出版社
EMERALD GROUP PUBLISHING LTD
DOI: 10.1108/HFF-02-2022-0076
关键词
Adomian decomposition method; Fractional differential equations; Adomian polynomials; Nonlinear Lienard's equation
The paper presents a new recursive scheme by combining the Adomian decomposition method with a magnificent recurrence formula to solve the initial-value problem of the general fractional differential equation of the nonlinear Lienard's equation. The proposed method offers advantages in computing and converges swiftly and accurately.
Purpose The purpose of this paper is to solve an initial-value problem for the general fractional differential equation of the nonlinear Lienard's equation. Design/methodology/approach A new recursive scheme is presented by combining the Adomian decomposition method with a magnificent recurrence formula and via the solutions of the well-known generalized Abel equation. Findings It is shown that the proposed method may offer advantages in computing the components yn; n = 1; 2; horizontal ellipsis in an easily computed formula. Also, the numerical experiments show that with few iterations of the recursive method, this technique converges swiftly and accurately. Originality/value The approach is original, and a reasonably accurate solution can be achieved with only two components. Moreover, the proposed method can be applied to several nonlinear models in science and engineering.
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