摘要:

AbstractBased on the implicit form of the finite difference analogue to the convection‐dispersion equation of variable velocity and dispersion coefficients, a highly accurate and stable explicit finite difference scheme has been developed by extending the von Rosenberg linear scheme to the varying cases. This variable velocity and dispersion coefficient scheme has been tested for the entire range of (2D/vΔx) between zero and unity, the region where no completely satisfactory numerical method has been previously available. No oscillations or numerical dispersion were observed in any of the solutio

ISSN:0749-159X    

DOI:10.1002/num.1690030202

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractA previously developed general procedure for deriving accurate difference equations to describe conditions at open boundaries for hyperbolic equations is extended and further illustrated by means of several examples of practical importance. Problems include those with both incoming and outgoing waves at the boundary, the use of locally cylindrical and spherical wave approximations at each point of the boundary, and nonlinear wave propagation. Reflected waves in all cases are minimal and less than 10−2of the incident wav

ISSN:0749-159X    

DOI:10.1002/num.1690030203

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractThe algebraic theory for numerical methods, as developed by Herrera [3–7], provides a broad theoretical framework for the development and analysis of numerical approximations. To this point, the technique has only been applied to ordinary differential equations with constant coefficients. The present work extends the theory by developing a methodology for equations with variable coefficients. Approximation of the coefficients by piecewise polynomials forms the foundation of the approach. Analysis of the method provides firm error estimates. Furthermore, the analysis points to particular procedures that produce optimal accuracy. Example calculations illustrate the computational procedure and verify the theoretical convergence rate

ISSN:0749-159X    

DOI:10.1002/num.1690030204

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractA convergence analysis is performed for an element‐partitioned subcycling algorithm for the semi‐discrete heat equation. It is shown that the algorithm generally attains first‐order rate‐of‐co

ISSN:0749-159X    

DOI:10.1002/num.1690030205

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690030201

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY