Showing papers in "Journal of Computational Physics in 1970"

TL;DR: In this article, a finite difference scheme for initial value problems of Fokker-Planck equations has been studied, which provides numerical solutions which preserve some of the more important intrinsic properties of the original partial differential equation.

TL;DR: In this article, the nonlinear properties of finite-amplitude water waves are modelled by a numerical method based on the Marker and Cell technique, which is shown to be a valid tool for analyzing incompressible flows with a free surface under transient conditions.

TL;DR: In this paper, several step-by-step methods for the numerical solution of coupled differential equations are given and compared under realistic circumstances, and a variant of the Numerov method is found to be the most efficient.

TL;DR: In this article, the so-called conservative or flux form of the finite difference formulation of convection terms is shown to be inadequate for preventing nonlinear instability in some cases, and a preferred scheme for the convection term which has the property of absolute spatial conservation is obtained.

TL;DR: In this article, a new method for numerical solution of the transient flow of viscous incompressible fluids having free surfaces is presented. The method is based on Lagrangian coordinates in contrast to other methods, which use the Eulerian representation.

TL;DR: In this paper, a rigorous treatment of the spatial grid is given, giving here a formulation which includes most codes now in use, and also the expressions for plasma properties are easily compared with the corresponding real plasma properties.

TL;DR: In this paper, two new methods for attaining convergence in self-consistent field calculations are described, which have been applied to semiconductor inversion layers at finite temperature, and have been shown to achieve a significant improvement in the performance.

TL;DR: Dilute gas transport properties calculation, investigating numerical techniques to minimize computation time to prescribed accuracy is described in this paper, where the authors propose a method to minimize the computational time to a prescribed accuracy.

TL;DR: Further development and refinement of the generalization of the Runge-Kutta method is given and extension to equations with three independent variables is extended.

TL;DR: In this paper, a method for finding physically reasonable parameters and confidence limits for parameters is described based on parameter scaling and diagonalization of the matrix of the normal equations, which is based on the assumption that the relationships provided by the observations are not really linearly independent when the random errors in the observations were considered.

TL;DR: In this paper, the authors approximate the potential in the one-dimensional Schrodinger equation by a step function with a finite number of steps, and the resulting differential equation has constant coefficients and is integrated exactly in terms of circular or hyperbolic functions.

TL;DR: In this paper, the nonlinear shallow-water equations in a rotating frame are integrated numerically over a sloping bottom with free lateral boundary conditions in such a way that the fluid determines its own level.

TL;DR: This paper describes a method for solving ordinary differential eigenvalue problems of the form N(u) + λM( u) = 0, where N and M are linear differential operators and u(x) is a scaler variable.

TL;DR: In this paper, a conformal mapping of the boundary of a closed two-dimensional region on the perimeter of a rectangular polygon in which is inscribed an orthogonal rectilinear grid is described.

TL;DR: In this paper, a linear numerical method is described which generates a curvilinear mesh that is as nearly orthogonal as possible, in a least-squares sense, subject to the constraint that mesh lines are matched to arbitrarily specified points around the perimeter of the region.

TL;DR: In this article, a dispersion relation for a computer-simulated plasma in which the effects of discreteness in space and time are treated exactly is derived, in the limit that the mesh spacing and the time step go to zero independently.

TL;DR: In this paper, the normal mode expansion technique is employed to obtain numerical results for the solution of the slab albedo problem in one-speed transport theory with anisotropic scattering.

TL;DR: In this paper, a comparison of Strang's schemes with the Richtmyer scheme and a generalization proposed by Gourlay and Morris [2] is reported, and several numerical experiments are conducted.

TL;DR: A system of programs in the language LISP 1.5 which handles all stages of calculation from the specification of an elementary-particle process in terms of a Hamiltonian of interaction or Feynman diagrams to the derivation of an absolute square of the matrix element for the process.

TL;DR: In this paper, Telenin's numerical method is adapted to the problem of steady supersonic flow past pointed conical bodies at yaw and formulated for cones of circular crosssections with the intention of determining bounded analytic solutions uniformly valid in the region between the shock and cone surfaces.

TL;DR: In this paper, a numerical model was developed to study the confinement of low-pressure plasmas in simple axially symmetric configurations, which contained the effects of resistivity, plasma inertia, and pressure gradients along the field.

TL;DR: In this paper, a finite difference scheme is constructed which has the property of simultaneously conserving total system mass, energy, and momentum throughout the interior of velocity space, thereby reducing nonconservation errors to boundary contributions only.

TL;DR: In this paper, the effectiveness of a finite difference scheme for solving problems in continuum mechanics is demonstrated by a series of problems ranging from elasticity theory to gas dynamics, and all of the results shown were plotted directly by the high speed computer and permit an easy evaluation of the technique.

TL;DR: In this paper, a new family of rational approximations to the matrix exponential is presented; the best member of the family to use depends upon the distribution of eigenvalues of A.

TL;DR: In this paper, a numerical integration or quadrature technique based on Richardson extrapolation to the trapezoidal rule as formulated by Romberg was developed and applied to evaluate some Fourier integrals which occur in the theory of an infinite cylindrical antenna.