Showing papers in "Journal of Computational Physics in 1974"

TL;DR: Fromm's second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms in this paper, where care is taken to keep the scheme in conservation form.

TL;DR: The Quiet Particle-Mesh model (QPM) as discussed by the authors uses a Gaussian-shaped charge cloud and careful shaping of the potential solution in either real or transform space, which is suitable for large collisionless plasma simulations with 10 5 or more particles.

TL;DR: In this paper, a method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of general multi-connected regions containing any number of arbitrarily shaped bodies is presented.

TL;DR: In this paper, the stability and accuracy of finite-difference approximations to simple linear PDEs are analyzed by studying the modified partial differential equation, which is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations.

TL;DR: In this article, a method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms is presented. But the method is only applicable to orthogonal coordinates and not to general tensor transformations.

TL;DR: In this article, the Dirichlet and Neumann conditions are applied to alternate components at the boundary of a model to eliminate reflections from the boundary by adding together the solutions of the Dirichelet and NN problems.

TL;DR: In this paper, a numerical method for predicting three-dimensional, steady viscous flow in ducts is described, which utilizes approximate governing equations which are applicable to flows having strong convection in one primary flow direction.

TL;DR: In this paper, the authors analyzed linear dispersion relations for one-dimensional, electromagnetic particle simulation codes in order to determine numerical stability properties and found that fast particles may resonate with light waves of matching phase velocity to produce a severe numerical instability.

TL;DR: In this article, a new numerical method for use in the solution of classical equations of motion is described, accurate to third order in the coordinates and second-order in the velocities, which has the unique property of preserving the energy and total linear and angular momenta at their initial values in the computation.

TL;DR: In this paper, a general two-dimensional theory for the choice of charge-sharing schemes in particle-mesh algorithms is presented, in which the lowest orders are represented by the familiar nearest-grid-point (NGP) and cloud-in-cell (CIC) schemes.

TL;DR: In this paper, the distribution function is expanded in a series of orthogonal polynomials, namely the Chebyshev polynomial, and the conditions under which this expansion is valid are discussed.

TL;DR: In this paper, higher-order difference schemes are considered for the numerical solution of Schroedinger's radial equation and an algorithm to find eigenvalues and eigenfunctions using one-directional "shooting" is discussed.

TL;DR: In this paper, it was shown that any nine-point second-order method obeying the conservation laws is a linear combination of two finite-element schemes, bilinear elements in rectangles and linear elements in triangles.

TL;DR: In this paper, the authors reviewed stability concepts arising in the numerical solution of ordinary differential equations in order to analyze their role in the classical solution of atomic and molecular scattering problems, and showed that treatment of dynamically stable systems is primarily required the use of stable integrators with small truncation errors.

TL;DR: In this paper, the question of extraneous boundary conditions in fluid dynamic computing was treated and several simple problems in one-dimensional gas dynamics were solved using different boundary schemes, and some surprising differences in the accuracy of the schemes were shown.

TL;DR: In this article, an algorithm for the numerical solution of inhomogeneous linear two-point boundary value problems using the method of invariant imbedding is presented, which handles the case in which the standard Riccati equation fails to have a solution over the entire interval of interest.

TL;DR: In this article, the authors compared second order schemes for hyperbolic systems with respect to stability properties and minimization of phase errors, and found that the Strang type splitting scheme, Leapfrog, and Lax-Wendroff (written as a two-step scheme) are the most stable schemes.

TL;DR: In this article, a procedure for numerical solution of convolution-type integral equations is presented, which uses a spectral representation of a transformed convolution operator and can be used to solve convolution equations with casual or non-casual kernels.

TL;DR: In this paper, the Fourier method was used to obtain a least square solution of the Poisson's equation on the surface of a sphere, which is economical in both computational time and storage.

TL;DR: In this paper, the authors treated the two-point boundary value problem as a multipoint boundary-value problem and applied the modified quasilinearization algorithm to solve it.

TL;DR: In this paper, a method for computing nontrivial solutions to the nonlinear partial differential equation ∇2Ψ + λ2sinh Ψ = 0, with λ = 0 on a square boundary is presented.

TL;DR: In this paper, a numerical solution for solving the wave equation in parabolic approximation is presented, based on cubic splines, which guarantee continuity of first and second derivatives of wave equation.

TL;DR: In this paper, the approximate recurrence of the initial state, observed recently in the numerical solution of Vlasov's equation by a finite-difference Eulerian model, is shown to be a property of three independent numerical methods.

TL;DR: In this paper, a fast direct Cauchy-Riemann solver was developed for solving the finite-difference equations representing systems of first-order elliptic partial differential equations in the form of the nonhomogeneous Cauché Riemann equations.

TL;DR: In this paper, it was shown that the truncation error of difference approximations is much larger on one side than on the other, and it oscillates in sign on the side where it is larger.

TL;DR: In this article, a numerical integration of the Vlasov equation replaces the continuous eigenvalue spectrum of the problem by a discrete spectrum, which can be represented by the eigen value spectrum of a finite matrix.

TL;DR: In this paper, a new fluid dynamics computing technique is described for the solution of time-varying multifluid flows in several space dimensions, referred to as the GILA method.

TL;DR: In this article, the authors proposed a method whereby only a fraction of the electromagnetic field grid need be in fast core at any given time, where the separate solutions may pertain to different time steps (jiggling) or the same time step (interlacing).

TL;DR: In this article, four finite difference schemes are applied to the numerical integration of the velocity field for low Reynolds number flows, within the framework of the MAC method, and numerical solutions are obtained for the square cavity problem at a Reynolds number equal to 10 −2.