Wendroff, Burton
Overview
Works:  21 works in 80 publications in 2 languages and 1,172 library holdings 

Genres:  Technical reports 
Roles:  Author 
Classifications:  QA297, 517.6 
Publication Timeline
.
Most widely held works by
Burton Wendroff
Theoretical numerical analysis by
Burton Wendroff(
Book
)
36 editions published between 1965 and 2014 in 3 languages and held by 643 WorldCat member libraries worldwide
36 editions published between 1965 and 2014 in 3 languages and held by 643 WorldCat member libraries worldwide
First principles of numerical analysis; an undergraduate text by
Burton Wendroff(
Book
)
13 editions published in 1969 in English and Undetermined and held by 358 WorldCat member libraries worldwide
13 editions published in 1969 in English and Undetermined and held by 358 WorldCat member libraries worldwide
Systems of conservation laws by
Peter D Lax(
Book
)
3 editions published between 1959 and 1960 in English and held by 6 WorldCat member libraries worldwide
In this paper a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws. Among these schemes we determine the best ones, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 23 meshpoints. These schemes are tested for stability and are found to be stable under a mild strengthening of the CourantFriedrichsLevy criterion. Test calculations of one dimensional flows of compressible fluids with shocks, rarefaction waves and contact discontinuities show excellent agreement with exact solutions. In particular, when Lagrange coordinates are used, there is no smearing of interfaces. The additional terms introduced into the difference scheme for the purpose of keeping the shock transition narrow are similar to, although not identical with, the artificial viscosity terms, and the like of them introduced by Richtmyer and von Neumann and elaborated by other workers in this field
3 editions published between 1959 and 1960 in English and held by 6 WorldCat member libraries worldwide
In this paper a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws. Among these schemes we determine the best ones, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 23 meshpoints. These schemes are tested for stability and are found to be stable under a mild strengthening of the CourantFriedrichsLevy criterion. Test calculations of one dimensional flows of compressible fluids with shocks, rarefaction waves and contact discontinuities show excellent agreement with exact solutions. In particular, when Lagrange coordinates are used, there is no smearing of interfaces. The additional terms introduced into the difference scheme for the purpose of keeping the shock transition narrow are similar to, although not identical with, the artificial viscosity terms, and the like of them introduced by Richtmyer and von Neumann and elaborated by other workers in this field
An unconditionally stable, finite difference method for photon transport problems by
Burton Wendroff(
Book
)
2 editions published in 1958 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1958 in English and held by 4 WorldCat member libraries worldwide
Finite difference approximations to solutions of partial differential equations by
Burton Wendroff(
Book
)
2 editions published in 1957 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1957 in English and held by 4 WorldCat member libraries worldwide
Theoretical numerical analysis by
Burton Wendroff(
)
1 edition published in 1966 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 4 WorldCat member libraries worldwide
The structure of certain finite difference schemes by
Burton Wendroff(
Book
)
2 editions published in 1960 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1960 in English and held by 4 WorldCat member libraries worldwide
Implicit radiation diffusion by Robert N Thorn(
Book
)
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
On the computation of the transport of radiation by
Burton Wendroff(
Book
)
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
Computing the critical frequencies of stepped shafts by
Burton Wendroff(
Book
)
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide
An unconditionally stable implicit difference scheme for the hydrodynamical equations by James Turner(
Book
)
3 editions published in 1964 in English and held by 3 WorldCat member libraries worldwide
We solve two hydrodynamical problems. The first involves a shock wave, a contact discontinuity, and a rarefaction wave using an unconditionally stable finite difference scheme. The Courant condition is satisfied everywhere except in one zone behind the shock, where it is violated by factors of 10 and 100. The nonlinear difference equations are solved by Newton's method. The total number of Newton iterations to get to a certain time is apparently independent of the degree to which the normal stability condition is violated in the one zone. The second problem involves two rarefaction waves moving in opposite directions. One wave moves in a region where the Courant condition is violated by a factor of approximately two. The other wave moves in a region where the Courant condition is satisfied. Numerical results are compared with the analytical solution. An examination of several runs indicates one explicit time step is about five times as fast as one implicit time step. Therefore, use of the implicit method is indicated when the Courant condition is violated by a factor of 5 or more
3 editions published in 1964 in English and held by 3 WorldCat member libraries worldwide
We solve two hydrodynamical problems. The first involves a shock wave, a contact discontinuity, and a rarefaction wave using an unconditionally stable finite difference scheme. The Courant condition is satisfied everywhere except in one zone behind the shock, where it is violated by factors of 10 and 100. The nonlinear difference equations are solved by Newton's method. The total number of Newton iterations to get to a certain time is apparently independent of the degree to which the normal stability condition is violated in the one zone. The second problem involves two rarefaction waves moving in opposite directions. One wave moves in a region where the Courant condition is violated by a factor of approximately two. The other wave moves in a region where the Courant condition is satisfied. Numerical results are compared with the analytical solution. An examination of several runs indicates one explicit time step is about five times as fast as one implicit time step. Therefore, use of the implicit method is indicated when the Courant condition is violated by a factor of 5 or more
First principles of numerical analysis : an undergraduate text by
Burton Wendroff(
)
1 edition published in 1969 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1969 in English and held by 3 WorldCat member libraries worldwide
Bounds for eigenvalues of some differential operators by the rayleighritz method(
Book
)
1 edition published in 1943 in English and held by 1 WorldCat member library worldwide
1 edition published in 1943 in English and held by 1 WorldCat member library worldwide
First Principles of numerical analysis: An undergraduate text : an undergraduate text by
Burton Wendroff(
Book
)
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
On the formulation and analysis of numerical methods for time dependent transport equations by
Herbert Bishop Keller(
Book
)
2 editions published between 1956 and 1957 in English and held by 1 WorldCat member library worldwide
2 editions published between 1956 and 1957 in English and held by 1 WorldCat member library worldwide
Convergence estimates for Galerkin methods for variable coefficient initialvalue problems by
Vidar Thomée(
Book
)
2 editions published in 1973 in English and held by 1 WorldCat member library worldwide
2 editions published in 1973 in English and held by 1 WorldCat member library worldwide
Finite difference approximations to solutions of partial differential equations by
Burton Wendroff(
)
1 edition published in 1958 in English and held by 1 WorldCat member library worldwide
1 edition published in 1958 in English and held by 1 WorldCat member library worldwide
A treatment of the dirichlet problem of potential theory by probability methods by
Burton Wendroff(
)
1 edition published in 1952 in English and held by 1 WorldCat member library worldwide
1 edition published in 1952 in English and held by 1 WorldCat member library worldwide
Systems of conversation laws by
Peter D Lax(
Book
)
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
Evolution, games, and learning : models for adaptation in machines and nature by International Conference of the Center for Nonlinear Studies(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
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Canada Conservation laws (Mathematics) Differential equations, HyperbolicNumerical solutions Differential equations, Partial Finite differences Heat equationNumerical solutions HydrodynamicsMathematical models Implicit functions Ionizing radiation Nuclear physics Numerical analysis Numerical calculations Photon transport theory Radiative transferMathematical models Scientists Shafting ShaftingBearings Transport theoryMathematical models United States
Alternative Names
Burton Wendroff American mathematician
Burton Wendroff Amerikaans wiskundige
Burton Wendroff amerikansk matematikar
Burton Wendroff amerikansk matematiker
Burton Wendroff matemático estadounidense
Burton Wendroff USamerikanischer Mathematiker
Wendroff, B.
Wendroff, B. (Burton)
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