SHALL 4 swMATH ID: 7 Software Authors: Navon, I.M.; Riphagen, H.A. Description: SHALL4 - an implicit compact fourth-order Fortran program for solving the shallow-water equations in conservation-law form. A FORTRAN IV computer program is documented implementing a compact fourth-order accurate finite difference scheme in a spatially factored form, for solving the nonlinear shallow-water equations on a limited domain. In contrast to the usual fourth-order schemes this compact fourth-order scheme requires the solution of only either block-tridiagonal or cyclic block-tridiagonal coefficient matrices. Moreover this compact fourth-order scheme is related to the finite-element method and has a smaller truncation error than the usual fourth-order schemes. The integral invariants of the shallow-water equations are calculated at each time-step and were determined to be well conserved during the numerical integration, ensuring that a realistic nonlinear structure is obtained. A Schumann-Wallington low-pass filtering procedure was incorporated in the program to overcome the increased aliasing due to the higher accuracy method. A third-order boundary condition is imposed, preserving the overall fourth-order convergence rate of the interior approximation. Homepage: http://people.sc.fsu.edu/~inavon/pubs1/exshall4.pdf Keywords: implicit compact fourth-order Fortran program; shallow-water equations; conservation-law form Related Software: FDL3DI Cited in: 4 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year SHALL 4 - an implicit compact fourth-order Fortran program for solving the shallow-water equations in conservation-law form. Zbl 0473.76030Navon, I. M.; Riphagen, H. A. 1981 all top 5 Cited by 10 Authors 1 Chemeda, H. Muleta 1 Chen, Yitung 1 Harley, Charis 1 Koroche, Kedir Aliyi 1 Li, Jichun 1 Liu, Guoqing 1 Momoniat, Ebrahim 1 Navon, Ionel Michael 1 Riphagen, H. A. 1 Sathinarain, M. Cited in 2 Serials 2 Computers & Mathematics with Applications 1 Iranian Journal of Numerical Analysis and Optimization Cited in 5 Fields 3 Numerical analysis (65-XX) 2 Partial differential equations (35-XX) 2 Fluid mechanics (76-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year