Document Zbl 1402.65073

Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping

Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity. (English) Zbl 1402.65073

ETNA, Electron. Trans. Numer. Anal. 48, 81-96 (2018).

The authors consider numerically solutions of the following nonlinear boundary value problem \[ \begin{aligned} &y^{(4)}+\alpha y'' +\beta y =f(y) +g(y),\quad x\in (0,1) \\ & y(0) =y(1)=y'' (0) =y'' (1)=0.\end{aligned} \] The Eigenvalue Expansion Method is used to obtain multiple solutions.

Reviewer: Serhiy Yanchuk (Berlin)

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34L10	Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

fourth-order ODEs; eigenfunction expansion method; system of polynomial equations; multiple solutions; homotopy continuation method

Software:

PHoM; PHCpack; HOM4PS; Bertini

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Full Text: DOI Link

References:

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