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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition (ADM), differential transform (DTM), least squares vector machines (LSSVMM), and ...
Hasan Ömür Özer +3 more
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Journal of Mathematics, 2023 This paper deals with the numerical solution of a class of highly oscillatory Volterra integral equations by collocation methods based on the exponential fitting technique.
S. Khudhair Abbas +2 more
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A Survey on Isogeometric Collocation Methods with Applications
Mathematics, 2023 Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin and collocation formulations. Exploiting
Jingwen Ren, Hongwei Lin
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Spectral collocation methods [PDF]
Applied Numerical Mathematics, 1989 This is a survey article on the application of spectral collocation methods to the solution of partial differential equations. For the most part, the basis functions used are either trigonometric or Chebyshev polynomials, although there is some discussion of Legendre polynomials.
Hussaini, M. Y. +2 more
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A pk-Adaptive Mesh Refinement for Pseudospectral Method to Solve Optimal Control Problem
IEEE Access, 2019 In this paper, a pk-adaptive mesh refinement of pseudospectral method is proposed for solving optimal control problem by using collocation at Legendre-Gauss-Lobatto (LGL) points, motivated by reducing the redundant collocation points in the state-of-art ...
Jun Huang +4 more
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Axioms, 2021 Nonlinear fractional differential equations are widely used to model real-life phenomena. For this reason, there is a need for efficient numerical methods to solve such problems.
Enza Pellegrino, Francesca Pitolli
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Boundary element collocation methods using splines with multiple knots [PDF]
, 1995 We extend the theory of boundary element collocation methods by allowing reduced inter-element smoothness (or in other words, by allowing trial functions that are splines with multiple knots).
Prößdorf, Siegfried, McLean, William
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Mathematics, 2021 Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem.
Mohammad Izadi +2 more
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Galerkin/Collocation Methods Based on 1D-Integrated-RBFNs for Viscoelastic Flows [PDF]
, 2010 In this paper, one-dimensional integrated radial-basis-function networks (1D-IRBFNs) are introduced into the Galerkin and point-collocation formulations to simulate viscoelastic flows.
N. Mai-Duy +5 more
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Mathematical Modelling and Analysis, 2014 In this paper, we deal with a system of linear and nonlinear integral algebraic equations (IAEs) of Hessenberg type. Convergence analysis of the discontinuous collocation methods is investigated for the large class of IAEs based on the new definitions ...
Babak Shiri
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