Note on the homotopy perturbation method for multivariate vector-value oscillatory integrals

DOI10.1016/j.amc.2009.04.048zbMath1177.65042OpenAlexW2029837441MaRDI QIDQ732449

Shuhuang Xiang, Ru-yun Chen

Publication date: 9 October 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.04.048

zbMATH Keywords

asymptotic methodnumerical examplesoscillatory integralshomotopy perturbation methodBessel transformation

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (10)

Fast integration for Cauchy principal value integrals of oscillatory kind ⋮ Numerical approximations to integrals with a highly oscillatory Bessel kernel ⋮ On the evaluation of Bessel transformations with the oscillators via asymptotic series of Whittaker functions ⋮ On evaluation of Bessel transforms with oscillatory and algebraic singular integrands ⋮ Asymptotic expansions of Bessel, Anger and Weber transformations ⋮ New algorithms for approximation of Bessel transforms with high frequency parameter ⋮ Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities ⋮ Spectral Levin-type methods for calculation of generalized Fourier transforms ⋮ Numerical computation of infinite Bessel transforms with high frequency ⋮ Galerkin-Levin method for highly oscillatory integrals

Cites Work

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• Numerical quadrature for Bessel transformations
• Numerical analysis of a fast integration method for highly oscillatory functions
• A homotopy method applied to elastica problems
• Application of He's homotopy perturbation method to Volterra's integro-differential equation
• Homotopy perturbation method for bifurcation of nonlinear problems
• Asymptotology by homotopy perturbation method
• Homotopy perturbation technique
• Application of He's homotopy perturbation method to nonlinear integro-differential equations
• Numerical solutions of highly oscillatory integrals
• On the quadrature of multivariate highly oscillatory integrals over non-polytope domains
• Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods
• An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems

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