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Asymptotic stability of the fundamental solution method
Journal of Computational and Applied Mathematics, 1991 The Dirichlet problem for the Laplace equation is considered in the circle \(| x|\rho\). The coefficients \(c_ k\) are found from the collocation system \(Ac=g\). An asymptotic estimate for the vector \(u=\Lambda c\) of the type \(\| u\| \leq Kn\| g\|\) is proved with norms related to the space \(R^ n\).
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Fractal and Fractional, 2022 In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy
Mojtaba Sajjadmanesh +3 more
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Inverse problem of incomplete boundaries and unknown parameters in two-dimensional Poisson equation
Nantong Daxue xuebao. Ziran kexue ban, 2022 The inverse problem of Poisson equation with incomplete boundary or unknown parameters have been solved by using the method of fundamental solutions (MFS) and Kalman filtering technique.
WANG Yue; JIANG Quan
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Lid-driven cavity flow using dual reciprocity [PDF]
MATEC Web of Conferences, 2020 The paper presents the use of the multi-domain dual reciprocity method of fundamental solutions (MD-MFSDR) for the analysis of the laminar viscous flow problem described by Navier-Stokes equations.
Mužík Juraj, Bulko Roman
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A Localized Method of Fundamental Solution for Numerical Simulation of Nonlinear Heat Conduction
Mathematics, 2022 In this study, an efficient localized method of fundamental solution (LMFS) is applied to nonlinear heat conduction with mixed boundary conditions. Since the thermal conductivity is temperature-dependent, the Kirchhoff transformation is used to transform
Feng Wang, Yan-Cheng Liu, Hui Zheng
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Journal of Marine Science and Engineering, 2023 The moving pseudo-boundary method of fundamental solutions (MFS) was employed to solve the Laplace equation, which describes the potential flow in a two-dimensional (2D) numerical wave tank.
Chengyan Wang +3 more
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Applicability and applications of the method of fundamental solutions [PDF]
Mathematics of Computation, 2009 Summary: We investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic systems. More specifically, we study whether linear combinations of fundamental solutions can approximate the solutions of the boundary value problems under consideration ...
Smyrlis, Yiorgos-Sokratis +1 more
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Axioms, 2023 The integro-differential Cauchy problem with exponential inhomogeneity and with a spectral value that turns zero at an isolated point of the segment of the independent variable is considered.
Burkhan Kalimbetov +2 more
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Frontiers in Physics, 2022 In this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented.
L Zhang +8 more
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A well conditioned Method of Fundamental Solutions
CoRR, 2021 The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and boundary conditions.
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