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Numerical Solution of Differential Equations by Repeated Quadratures
SIAM Review, 1964exaly +2 more sources
On the solution of the thomas-fermi equation by differential quadrature
Journal of Computational Physics, 1984This paper presents a method of finding approximate solutions to the Thomas-Fermi equation \(d^ 2f/dx^ 2=f^{3/2}/x^{1/2}\) with \(f=1\) at \(x=0\) and \(f=0\) as \(x\to \infty\). The essential approximation used is that for any linear operator L \(L(f(x_ i))\simeq \sum^{N}_{j=1}W_{ij}f(x_ j),\) \(i=1,2,...,N\) where \(x_ i\) are sample points and \(W_ ...
Civan, Faruk, Sliepcevich, C. M.
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Solution of the Poisson equation by differential quadrature
International Journal for Numerical Methods in Engineering, 1983AbstractThe method of differential quadrature is demonstrated by solving the two‐dimensional Poisson equation. The results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the Galerkin, the control‐volume and the five‐point finite difference methods.
Civan, Faruk, Sliepcevich, C. M.
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A quadrature method for numerical solutions of fractional differential equations
Applied Mathematics and Computation, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mujeeb ur Rehman +2 more
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Acoustic Scattering Problems with Convolution Quadrature and the Method of Fundamental Solutions
Communications in Computational Physics, 2021Time-domain acoustic scattering problems in two dimensions are studied. The numerical scheme relies on the use of the Convolution Quadrature (CQ) method to reduce the time-domain problem to the solution of frequency-domain Helmholtz equations with complex wavenumbers.
Labarca, Ignacio +1 more
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The Quadrature Discretization Method (QDM) in the solution of the Schrödinger equation
Journal of Mathematical Chemistry, 1998The main purpose of this paper is to consider the solutions of one-dimensional Schrödinger equation with the quadrature discretization method [cf. \textit{B. D. Shizgal} and \textit{H. Chen}, J. Chem. Phys. 104, 4137 (1996)]. The applications to four potential functions considered recently by several other researchers are presented. The eigenvalues and
Chen, Heli, Shizgal, Bernie D.
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Solution of poisson and laplace equations by quadrilateral quadrature element
International Journal of Solids and Structures, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhong, Hongzhi, He, Yuhong
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Solution by quadratures of certain ordinary differential equations
International Journal of Mathematical Education in Science and Technology, 1984This paper discusses methods that are applicable in the solution by quadratures of linear second‐order differential equations with variable coefficients. These same techniques, when applied to equations with constant coefficients, produce an extremely useful method in the teachingof ordinary differential equations.
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Solutions in quadratures to the CEV model
International Journal of Financial Engineering and Risk Management, 2019Cox introduced the constant elasticity of variance (CEV) model in 1975, in order to capture this inverse relationship between the stock price and its volatility. An important parameter in the model is the parameter β, the elasticity of volatility. We use Kovacic's algorithm to derive, for all half-integer values of β, all solutions 'in quadratures' of ...
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Solution of Helmholtz equation by differential quadrature method
Computer Methods in Applied Mechanics and Engineering, 1999The polynomial-based differential quadrature and the Fourier expansion-based differential quadrature methods are examined for the two-dimensional Helmholtz equation. Examples indicate that 2 to 3 grid points per wavelength suffice.
Shu, C., Xue, H.
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