A Study of the Numerical Solution of Partial Differential Equations
From MaRDI portal
Publication:5803628
DOI10.1002/sapm1950291223zbMath0042.13204OpenAlexW2325298721MaRDI QIDQ5803628
Sidney Kaplan, Morton A. Hyman, George G. O'Brien
Publication date: 1951
Published in: Journal of Mathematics and Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/sapm1950291223
Related Items
On the Convergence of a Solution of a Difference Equation to a Solution of the Equation of Diffusion ⋮ Unnamed Item ⋮ The cell Reynolds number myth ⋮ Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique ⋮ A compact unconditionally stable finite-difference method for transient one-dimensional advection-diffusion ⋮ Some three-level finite difference methods for simulating advection in fluids ⋮ Über zwei Differenzenverfahren der Grenzschichttheorie ⋮ An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation ⋮ Time‐space method for multidimensional melting and freezing problems ⋮ An error propagation in the numerical literature ⋮ A new third-order finite-difference method for transient one-dimensional advection—diffusion ⋮ Downstream implicit schemes for advection ⋮ Application of the \(\varTheta\)-method to a telegraphic model of fluid flow in a dual-porosity medium ⋮ An optimum SOR procedure for the solution of elliptic partial differential equations with any domain or coefficient set ⋮ Redefined quintic B-spline collocation technique for nonlinear higher order PDEs ⋮ A direct approach to the problem of stability in the numerical solution of partial differential equations ⋮ Higher-order accurate two-step finite difference schemes for the many-dimensional wave equation ⋮ Survey of the stability of linear finite difference equations ⋮ Identification of time‐dependent potential in a fourth‐order pseudo‐hyperbolic equation from additional measurement ⋮ Convergence, accuracy and stability of finite element approximations of a class of non‐linear hyperbolic equations ⋮ Numerical Solution of Boundary Value Problems ⋮ A comparative study of finite difference methods for solving the one- dimensional transport equation with an initial-boundary value discontinuity ⋮ Conditionally stable difference approximations for the wave-operator ⋮ Sparse identification of truncation errors ⋮ Explicit three-point three-level FDMS for the one-dimensional constant- coefficient advection-diffusion equation ⋮ Mixed explicit-implicit iterative finite element scheme for diffusion-type problems: II. Solution strategy and examples ⋮ Mixed explicit-implicit iterative finite element scheme for diffusion-type problems: I. Theory ⋮ From finite differences to finite elements. A short history of numerical analysis of partial differential equations ⋮ Comparative study of six explicit and two implicit finite difference schemes for solving one-dimensional parabolic partial differential equations ⋮ Dynamic analysis of structural deformation and metal forming ⋮ Engineering applications of ADI methods to piecewise linear multidimensional heat transfer ⋮ A finite difference scheme for the incompressible advection-diffusion equation ⋮ Approximation of the Crank-Nicolson method by the iterated dynamic-theta method ⋮ Time-dependent laminar incompressible flow through a spherical cavity ⋮ Stability of the centred finite difference scheme for the three‐dimensional equations of elastodynamics ⋮ Modeling the propagation of elastic waves using a modified finite difference grid. ⋮ A numerical method for two-dimensional Navier-Stokes equation by multi-point finite differences ⋮ Difference method for wave analysis of the split Hopkinson pressure bar with a viscoelastic specimen ⋮ On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables ⋮ On the solution of nonlinear hyperbolic differential equations by finite differences ⋮ Convergence of Finite Difference Solutions to a Solution of the Equation of the Vibrating Rod ⋮ On integration of parabolic equations by difference methods: I. Linear and quasi‐linear equations for the infinite interval ⋮ Non-iterative numerical solution of boundary-value problems ⋮ Explicit difference approximations of the one-dimensional diffusion equation, using a smoothing technique ⋮ On Unsteady Flow of Compressible Viscous Fluids ⋮ Explicit difference approximations of the one-dimensional diffusion equations, using a smoothing technique ⋮ A discrete-variable approach for elastic-plastic wave motions in layered solids ⋮ Explicit finite difference methods for variable velocity advection in the presence of a source ⋮ Stability of finite difference approximations to a diffusion-convection equation ⋮ The Application of Stability Analysis in the Numerical Solution of Quasi-Linear Parabolic Differential Equations ⋮ Über die Lösung des Cauchyproblems für lineare partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. I: Stabile Systeme von Differenzengleichungen ⋮ Solution of the two-dimensional, unsteady, compressible Navier-Stokes equations using a second-order accurate numerical scheme ⋮ Numerical solution of systems of mixed partial differential equations associated with transport phenomena with exchange ⋮ Explicit Solutions of the One-Dimensional Heat Equation for a Composite Wall ⋮ On Integration of Quasi-Linear Parabolic Equations By Explicit Difference Methods ⋮ Calculation of Transient Motion of Submerged Cables ⋮ Some thoughts on shell modelling for crash analysis ⋮ 33 years of numerical instability. I ⋮ Unnamed Item ⋮ An inverse problem of fourth-order partial differential equation with nonlocal integral condition ⋮ A theoretical proof of the invalidity of dynamic relaxation arc-length method for snap-back problems
This page was built for publication: A Study of the Numerical Solution of Partial Differential Equations