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Sinc-Galerkin method for numerical solution of the Bratu’s problems
Numerical Algorithms, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jalil Rashidinia +2 more
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1993
The formulas of the previous chapter are all related to the Cardinal function representation $$C(f,\,h)\, \circ \,\phi (x)\, = \,\mathop \sum \limits_{k = - \infty }^\infty \,F({z_k})\,S(k,h)\, \circ \,\phi (x),$$ (5.1.1) ; with \({z_k}\, = \,{\phi ^{ - 1}}(kh)\).
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The formulas of the previous chapter are all related to the Cardinal function representation $$C(f,\,h)\, \circ \,\phi (x)\, = \,\mathop \sum \limits_{k = - \infty }^\infty \,F({z_k})\,S(k,h)\, \circ \,\phi (x),$$ (5.1.1) ; with \({z_k}\, = \,{\phi ^{ - 1}}(kh)\).
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1995
In this section we derive several methods of approximation using the function values {f(kh)}∞k=- ∞ . We present a family of simple rational functions, which make possible the explicit and arbitrarily accurate rational approximation of the filter, the step (Heaviside) and the impulse (delta) functions.
Marek A. Kowalski +2 more
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In this section we derive several methods of approximation using the function values {f(kh)}∞k=- ∞ . We present a family of simple rational functions, which make possible the explicit and arbitrarily accurate rational approximation of the filter, the step (Heaviside) and the impulse (delta) functions.
Marek A. Kowalski +2 more
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The Sinc method in multiple space dimensions: Model problems
Numerische Mathematik, 1989The sinc-Galerkin method lies on the use of orthogonal basis S(k,h)(x)\(\equiv \sin c(x-kh/h)\), \(x\in {\mathbb{R}}\), \(h>0\), \(k\in {\mathbb{Z}}\), where the sinc function is given by sinc(x)\(\equiv \sin (\pi x)/\pi x\), \(x\in {\mathbb{R}}\). Corresponding numerical methods including the sinc- Galerkin method have been analyzed by F.
McArthur, Kelly M. +2 more
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A Sinc‐collocation method with boundary treatment for the Stokes equations
International Journal for Numerical Methods in Fluids, 2006AbstractIn Stokes equations the velocity u and the pressure p are coupled together by the imcompressibility condition div u=0 which makes the equations difficult to solve numerically. In this paper, a method named Sinc‐collocation method with boundary treatment (SCMBT) is applied to the Stokes equations. The numerical results show that our method is of
Li, Chen, Wu, Xionghua
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Solving Bratu's problem by double exponential sinc method
2020Summary: In this study, improved Sinc-Galerkin and Sinc-collocation methods are developed based on double exponential transformation to solve a one-dimensional Bratu-type equation. The properties of these methods are used to reduce the solution of the nonlinear problem to the solution of nonlinear algebraic equations.
Nabati, Mohammad, Nikmanesh, Soudabeh
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Sinc Methods for Lévy–Schrödinger Equations
2021We shall examine the fractional generalization of the eigenvalue problem of Schrodinger’s equation for one dimensional problems in connection with Levy stable probability distributions. The corresponding Sturm–Liouville (SL) problem for the fractional Schrodinger equation is formulated and solved on \(\mathbb {R}\) satisfying natural Dirichlet boundary
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Discontinuous Galerkin methods using poly-sinc approximation
Mathematics and Computers in Simulation, 2021Omar A Khalil, Gerd Baumann
exaly
Convergence rate estimation of poly-Sinc-based discontinuous Galerkin methods
Applied Numerical Mathematics, 2021Omar A Khalil, Gerd Baumann
exaly