Results 11 to 20 of about 73,046 (353)

Numerical integration methods of the Vlasov equation [PDF]

Journal of Computational Physics, 1971
Abstract The methods of integrating the nonlinear Vlasov equation are reviewed, compared and interrelations are investigated. Another method is given which allows a truncation of the resulting infinite matrix without causing numerical instabilities. Its application to the linear and nonlinear Vlasov equation is discussed.
Glenn Joyce, Georg Knorr, Homer K Meier
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A numerical method for multidimensional Volterra integral equations

Applied Mathematical Sciences, 2022
In this paper, we introduce a new numerical procedure to solve multi-dimensional Volterra integral equations, based on the weighted mean-value theorem. Our method allows to determine a system of nonlinear equations, where the rst one is obtained via the application of the theoretical results, and the remaining ones are built through a Picard-like ...
Immacolata Oliva, Antonio Luciano Martire   +1 more
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A method for the numerical integration of ordinary differential equations [PDF]

Mathematics of Computation, 1958
where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments xi in (x0, xo + h)-hence we require the values of y(x) at these arguments.
Stoller, L., Morrison, D.
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On the Numerical Integration of Ordinary Differential Equations by Processed Methods [PDF]

SIAM Journal on Numerical Analysis, 2004
A one-step integrator \(\psi_h: \mathbb{R}^D\to \mathbb{R}^D\) with time step \(h\) for an ordinal differential equation \(x'= f(x)\), \(f: \mathbb{R}^D\to \mathbb{R}^D\), can be enhanced by ``processing'' based on a postprocessors \(\pi_h: \mathbb{R}^D\to \mathbb{R}^D\), to obtain a new integrator \(\widehat\psi_h:=\pi_h\circ\psi_h\circ \pi^{-1}_h ...
Sergio Blanes, Fernando Casas, Ander Murua   +2 more
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The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations

Journal of Chemistry, 2020
In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports.
Xiaoyan Liu, Jin Xie, Zhi Liu, Jiahuan Huang   +3 more
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An Effective Local Radial Basis Function Method for Solving the Delay Volterra Integral Equation of Nonvanishing and Vanishing Types

Journal of Mathematics, 2022
This paper presents a numerical method for solving a class of the delay Volterra integral equation of nonvanishing and vanishing types by applying the local radial basis function method.
Neda Khaksari, Mahmoud Paripour, Nasrin Karamikabir   +2 more
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Volterra integral equations and fractional calculus: Do neighbouring solutions intersect? [PDF]

, 2012
This is the author's PDF version of an article published in Journal of Integral Equations and Applications. The definitive version is available at rmmc.asu.edu/jie/jie.html.This journal article considers the question of whether or not the solutions to ...
Diethelm, Kai, Ford, Neville J.
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An Innovative Approach to Nonlinear Fractional Shock Wave Equations Using Two Numerical Methods

Mathematics, 2023
In this research, we propose a combined approach to solving nonlinear fractional shock wave equations using an Elzaki transform, the homotopy perturbation method, and the Adomian decomposition method. The nonlinear fractional shock wave equation is first
Meshari Alesemi
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Conservative numerical methods for model kinetic equations [PDF]

, 2007
A new conservative discrete ordinate method for nonlinear model kinetic equations is proposed. The conservation property with respect to the collision integral is achieved by satisfying at the discrete level approximation conditions used in deriving the ...
Titarev, Vladimir A.
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A New Method of Numerical Integration of Differential Equations [PDF]

Mathematics of Computation, 1964
L'A. propose une méthode d'intégration approchée de \(y'=f(x, y)\) dans laquelle \(y'\) est évalué par extrapolation au début du pas et par substitution au milieu. Un exemple est donné. La méthode utilise, comme l'avait suggéré l'A. de cette analyse, à la fois le principe de Runge-Kutta et celui des méthodes à pas liés.
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