Mixed meshless local Petrov–Galerkin (MLPG) collocation methods for gradient elasticity theories of Helmholtz type
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DOI: 10.1007/s00466-020-01866-6
Abstract: Two mixed meshless collocation methods for solving problems by considering a linear gradient elasticity theory of the Helmholtz type are proposed. The solution process is facilitated by employing operator-split procedures, splitting the original 4th-order problem… read more here.
Keywords: elasticity; helmholtz type; gradient elasticity; collocation methods ... See more keywords
Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities
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DOI: 10.1016/j.apnum.2019.12.013
Abstract: Abstract Filon collocation methods are well known for their good performances in solving the second-kind highly oscillatory Volterra integral equations with weak singularities. As the frequency increases, these methods can provide much more accurate solutions… read more here.
Keywords: frequency; highly oscillatory; collocation methods; volterra integral ... See more keywords
Modified Legendre rational and exponential collocation methods for solving nonlinear Hammerstein integral equations on the semi-infinite domain
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DOI: 10.1080/00207160.2022.2033236
Abstract: This paper discusses two efficient collocation methods for solving the Hammerstein integral equations on the semi-infinite domain, where the underlying solutions decay to zero at infinity. These methods are based upon modified Legendre rational and… read more here.
Keywords: semi infinite; methods solving; collocation methods; hammerstein integral ... See more keywords
Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels
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DOI: 10.1080/00207160.2023.2203786
Abstract: In this paper two collocation methods, the direct linear interpolation collocation method and the direct high order interpolation collocation method, are proposed to solve the second kind of Volterra integral equations with weakly singular highly… read more here.
Keywords: highly oscillatory; collocation methods; interpolation collocation; collocation ... See more keywords
Discontinuous collocation methods and gravitational self-force applications
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DOI: 10.1088/1361-6382/abdf27
Abstract: Numerical simulations of extreme mass ratio inspirals, the most important sources for the LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory… read more here.
Keywords: discontinuous collocation; force; collocation methods; gravitational self ... See more keywords
Domain-type RBF Collocation Methods for Biharmonic Problems
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DOI: 10.1142/s0219876218500780
Abstract: In this paper some meshless, domain-type discretization techniques are investigated in the context of problems modeled by biharmonic equations. These numerical methods use interpolant composed of radial basis functions (RBFs) as well as collocation technique… read more here.
Keywords: rbf collocation; collocation; domain type; collocation methods ... See more keywords
Improved RBF Collocation Methods for Fourth Order Boundary Value Problems
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DOI: 10.4208/cicp.oa-2019-0163
Abstract: Radial basis function (RBF) collocation methods (RBFCMs) are applied to fourth order boundary value problems (BVPs). In particular, we consider the classical Kansa method and the method of approximate particular solutions (MAPS). In the proposed… read more here.
Keywords: fourth order; value; collocation; order boundary ... See more keywords