Results 21 to 30 of about 147,119 (311)
Adaptive meshless centres and RBF stencils for Poisson equation [PDF]
, 2011 We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are
Oleg Davydov +3 more
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On spherical averages of radial basis functions [PDF]
, 2008 A radial basis function (RBF) has the general form $$s(x)=\sum_{k=1}^{n}a_{k}\phi(x-b_{k}),\quad x\in\mathbb{R}^{d},$$ where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric
Baxter, Brad J.C.
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Branches of Radial Solutions for Semipositone Problems
Journal of Differential Equations, 1995 Let \(\Omega\) be the unit ball in \(\mathbb{R}^N\) \((N> 1)\) centered at the origin, \(f: \mathbb{R}\to \mathbb{R}\) a differentiable, monotone function such that \(f(0)< 0\), \(\lim_{d\to \infty} {f(x)\over d}= \infty\), \(F(d)- {N- 2\over 2N} df(d)\geq M\) for all \(d\in \mathbb{R}\), where \(M\in \mathbb{R}\), \(F(d)= \int^d_0 f(s) ds\) and ...
Castro, Alfonso +2 more
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Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method [PDF]
, 2020 In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excited phase (NEP) equation (a single sixth-order nonlinear partial differential equation) using a more advanced numerical method, namely, the integrated radial ...
Strunin, Dmitry +7 more
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Radial solutions of the elliptic Liouville equation
Results in Physics, 2021 In this paper, we derive new closed-form radial solutions for the following elliptic Liouville equation △ϕ+φ(x)eϕ=0inΩ⊂Rn,and its generalized equation △ϕ+φ(x)eϕ=f(x)inΩ⊂Rn,where △ is the Laplace operator, φ and f are smooth positive functions.
Lazhar Bougoffa, Ammar Khanfer
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Radial solutions for a Dirichlet problem in a ball
Journal of Differential Equations, 1985 Let \(\Omega \subset {\mathbb{R}}^ N\) be a bounded smooth domain. Let \(\lambda_ 1\) be the first eigenvalue of -\(\Delta\) on \(H^ 1_ 0(\Omega)\) and let \(\Phi_ 1>0\) be a corresponding eigenfunction. The Ambrosetti-Prodi problem \[ (1)\quad -\Delta u=f(x,u)+h(x)+t\Phi_ 1(x)\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega, \] where \(t\in
Costa, D.G, de Figueiredo, D.G
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Genetic programming approaches for solving elliptic partial differential equations [PDF]
, 2008 In this paper, we propose a technique based on genetic programming (GP) for meshfree solution of elliptic partial differential equations. We employ the least-squares collocation principle to define an appropriate objective function, which is optimized ...
Sobester, A. +5 more
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The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
Journal of Mathematics, 2021 The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution.
Juan Zhang +3 more
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Radial solutions to the wave equation [PDF]
Annali di Matematica Pura ed Applicata, 2002 The authors study the Cauchy problem \[ \begin{gathered} \frac{\partial^2u}{\partial t^2}(t,x) =\frac{\partial^2u}{\partial x^2}(t,x) +\frac{2\alpha+1}{x}\frac{\partial u}{\partial x}(t,x),\\ u(0,x)=\phi(x),\,\,\,\frac{\partial u}{\partial x}(0,x)=\psi(x), \end{gathered} \] where \(\alpha\geq -1/2\) and ...
COLZANI, LEONARDO +2 more
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Radial and non-radial solutions for a nonlinear Schrodinger equation with a constraint
Electronic Journal of Differential Equations, 2021 We study the classical nonlinear Schodinger equation with a radially symmetric potential and a constraint, for the mass subcritical case. We obtain conditions that assure the existence of non-radial solutions. Also we show symmetry breaking of the ground states, and the existence of multiple non-radial solutions under additional conditions. Folr ...
Jiaxuan Yang +2 more
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