Finite Difference Techniques for Partial Differential Equations

[1]  R. E. Smith,et al.  Algebraic grid generation , 1987 .

[2]  D. Ives,et al.  Orthogonal grid generation , 1984 .

[3]  M. Visbal,et al.  Generation of orthogonal and nearly orthogonal coordinates with gridcontrol near boundaries , 1982 .

[4]  J. Steger,et al.  Generation of Body-Fitted Coordinates Using Hyperbolic Partial Differential Equations , 1980 .

[5]  R. Sorenson.  A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation , 1980 .

[6]  Peter R. Eiseman,et al.  A multi-surface method of coordinate generation , 1979 .

[7]  W. Thacker,et al.  Irregular Grid Finite-Difference Techniques: Simulations of Oscillations in Shallow Circular Basins , 1977 .

[8]  D. Ives,et al.  A Modern Look at Conformal Mapping Including Multiply Connected Regions , 1976 .

[9]  G. de Vahl Davis,et al.  An evaluation of upwind and central difference approximations by a study of recirculating flow , 1976 .

[10]  J. Trapp,et al.  A simple heuristic method for analyzing the effect of boundary conditions on numerical stability , 1976 .

[11]  Richard C. J. Somerville,et al.  On the use of a coordinate transformation for the solution of the Navier-Stokes equations , 1975 .

[12]  R. F. Warming,et al.  The modified equation approach to the stability and accuracy analysis of finite-difference methods , 1974 .

[13]  E. J. Harrison,et al.  Three-Dimensional Numerical Simulations of Tropical Systems Utilizing Nested Finite Grids , 1973 .

[14]  Roland A. Sweet,et al.  Mesh refinements for parabolic equations , 1973 .

[15]  S. Venit.  Mesh refinements for parabolic equations of second order , 1973 .

[16]  Eugenia Kálnay de Rivas.  On the use of nonuniform grids in finite-difference equations , 1972 .

[17]  P. Roache,et al.  Nonuniform mesh systems , 1971 .

[18]  C. Dalton,et al.  Errors in the use of nonuniform mesh systems , 1971 .

[19]  Richard A. Anthes,et al.  NUMERICAL EXPERIMENTS WITH A TWO-DIMENSIONAL HORIZONTAL VARIABLE GRID , 1970 .

[20]  S. Osher.  Mesh Refinements for the Heat Equation , 1970 .

[21]  G. Moretti,et al.  Numerical analysis of viscous one-dimensional flows☆ , 1970 .

[22]  George Veronis,et al.  A simple finite-difference grid with non-constant intervals , 1970 .

[23]  S. I. Cheng,et al.  Numerical Integration of Navier-Stokes Equations , 1970 .

[24]  David L. Williamson,et al.  NUMERICAL INTEGRATION OF FLUID FLOW OVER TRIANGULAR GRIDS , 1969 .

[25]  A. A. Szewczyk,et al.  Time‐Dependent Viscous Flow over a Circular Cylinder , 1969 .

[26]  S. Chavez,et al.  Numerical Study of the Coanda Effect. , 1969 .

[27]  G. Kusic.  On stability of numerical methods for systems of initial-value partial differential equations , 1969 .

[28]  P. Morel,et al.  A FINITE-DIFFERENCE APPROXIMATION OF THE PRIMITIVE EQUATIONS FOR A HEXAGONAL GRID ON A PLANE , 1969 .

[29]  A. Lavi,et al.  Stability of difference methods for initial-value type partial differential equations , 1969 .

[30]  K. E. Torrance,et al.  Comparison of finite-difference computations of natural convection , 1968 .

[31]  C. W. Hirt.  Heuristic stability theory for finite-difference equations☆ , 1968 .

[32]  Enzo O. Macagno,et al.  Laminar eddies in a two-dimensional conduit expansion , 1966 .

[33]  N. O. Weiss,et al.  Convective difference schemes , 1966 .

[34]  C. Pearson.  Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks , 1965, Journal of Fluid Mechanics.

[35]  Carl E. Pearson,et al.  A computational method for viscous flow problems , 1965, Journal of Fluid Mechanics.

[36]  P. Lax,et al.  Difference schemes for hyperbolic equations with high order of accuracy , 1964 .

[37]  Jacob E. Fromm,et al.  Numerical Solution of the Problem of Vortex Street Development , 1963 .

[38]  J. J. Douglas.  Alternating direction methods for three space variables , 1962 .

[39]  P. L. T. Brian,et al.  A finite‐difference method of high‐order accuracy for the solution of three‐dimensional transient heat conduction problems , 1961 .

[40]  P. Lax,et al.  Systems of conservation laws , 1960 .

[41]  R. B. Payne,et al.  Calculations of unsteady viscous flow past a circular cylinder , 1958, Journal of Fluid Mechanics.

[42]  Susan G. Hahn.  Stability criteria for difference schemes , 1958 .

[43]  Jim Douglas,et al.  A note on the alternating direction implicit method for the numerical solution of heat flow problems , 1957 .

[44]  R. D. Richtmyer,et al.  Survey of the stability of linear finite difference equations , 1956 .

[45]  Stephen H. Crandall,et al.  An optimum implicit recurrence formula for the heat conduction equation , 1955 .

[46]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[47]  J. J. Douglas.  On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods , 1955 .

[48]  W. Wasow.  Discrete approximations to elliptic differential equations , 1955 .

[49]  S. Frankel,et al.  Stability conditions in the numerical treatment of parabolic differential equations , 1953 .

[50]  R. Courant,et al.  On the solution of nonlinear hyperbolic differential equations by finite differences , 1952 .

[51]  Fritz John,et al.  On integration of parabolic equations by difference methods: I. Linear and quasi‐linear equations for the infinite interval , 1952 .

[52]  S. Frankel.  Convergence rates of iterative treatments of partial differential equations , 1950 .

[53]  George G. O'Brien,et al.  A Study of the Numerical Solution of Partial Differential Equations , 1950 .

[54]  Pentti Laasonen,et al.  Über eine Methode zur Lösung der Wärmeleitungs-gleichung , 1949 .

[55]  H. Stommel,et al.  The westward intensification of wind‐driven ocean currents , 1948 .

[56]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947, Mathematical Proceedings of the Cambridge Philosophical Society.

[57]  L. J. Comrie,et al.  Mathematical Tables and Other Aids to Computation. , 1946 .

[58]  L. Fox,et al.  Solution by relaxation methods of plane potential problems with mixed boundary conditions , 1944 .

[59]  Fritz John,et al.  On Integration of Parabolic Equations By Difference Methods , 1985 .

[60]  R. May,et al.  The Numerical Solution of Ordinary Differential Equations: Initial Value Problems , 1984 .

[61]  Z. U. A. Warsi,et al.  Basic differential models for coordinate generation , 1982 .

[62]  Christo I. Christov,et al.  Orthogonal coordinate meshes with manageable Jacobian , 1982 .

[63]  S. Nakamura,et al.  Marching grid generation using parabolic partial differential equations , 1982 .

[64]  R. Davis,et al.  Solution of viscous internal flows on curvilinear grids generated by the Schwarz-Christoffel transformation , 1982 .

[65]  A Roberts,et al.  Automatic topology generation and generalised B spline mapping , 1982 .

[66]  James M. Hyman,et al.  The numerical differentiation of discrete functions using polynomial interpolation methods , 1982 .

[67]  Joe F. Thompson.  Elliptic grid generation , 1982 .

[68]  P. D. Thomas,et al.  Construction of composite three dimensional grids from subregion grids generated by elliptic systems , 1981 .

[69]  R. May,et al.  Three-dimensional numerical model of tides in Spencer Gulf , 1981 .

[70]  L. Eriksson,et al.  Three dimensional spline-generated coordinate transformations for grids around wing-body configurations , 1980 .

[71]  D. A. Caughey,et al.  A systematic procedure for generating useful conformal mappings , 1978 .

[72]  A. H. Moore,et al.  A comparison of Crandall and Crank–Nicolson methods for solving a transient heat conduction problem , 1975 .

[73]  W. J. Gordon,et al.  Construction of curvilinear co-ordinate systems and applications to mesh generation , 1973 .

[74]  Robert W. MacCormack,et al.  Numerical solution of the interaction of a shock wave with a laminar boundary layer , 1971 .

[75]  Kálnay de Rivas,et al.  The circulation of the atmosphere of Venus , 1971 .

[76]  N. N. I︠A︡nenko.  The Method of Fractional Steps: The Solution of Problems of Mathematical Physics in Several Variables , 1971 .

[77]  A. A. Samarskii.  Local one-dimensional difference schemes for multi-dimensional hyperbolic equations in an arbitrary region☆ , 1964 .

[78]  Ye.G. D'yakonov.  Difference schemes with a separable operator for general second order parabolic equations with variable coefficients , 1964 .

[79]  B. A. Carré,et al.  The Determination of the Optimum Accelerating Factor for Successive Over-relaxation , 1961, Comput. J..

[80]  R. Varga,et al.  Implicit alternating direction methods , 1959 .

[81]  D. Young.  Iterative methods for solving partial difference equations of elliptic type , 1954 .

[82]  L. Richardson.  The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .