FAST INTEGRATION OF ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

Rafael G. Campos () and Rafael García Ruiz ()
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Rafael G. Campos: Facultad de Ciencias Físico-Matemáticas, Edificio Alfa, Universidad Michoacana, 58060, Morelia, Michoacán, México
Rafael García Ruiz: Facultad de Ciencias Físico-Matemáticas, Edificio Alfa, Universidad Michoacana, 58060, Morelia, Michoacán, México

International Journal of Modern Physics C (IJMPC), 2013, vol. 24, issue 11, 1-10

Abstract: Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions ofL2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

Keywords: Spectral methods; differentiation matrices; fast Fourier transform; boundary value problems; solitons; 02.60.Lj; 02.60.Jh; 02.70.Hm; 02.60.Jn (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0129183113500824

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