SHALL 4
swMATH ID:  7 
Software Authors:  Navon, I.M.; Riphagen, H.A. 
Description:  SHALL4  an implicit compact fourthorder Fortran program for solving the shallowwater equations in conservationlaw form. A FORTRAN IV computer program is documented implementing a compact fourthorder accurate finite difference scheme in a spatially factored form, for solving the nonlinear shallowwater equations on a limited domain. In contrast to the usual fourthorder schemes this compact fourthorder scheme requires the solution of only either blocktridiagonal or cyclic blocktridiagonal coefficient matrices. Moreover this compact fourthorder scheme is related to the finiteelement method and has a smaller truncation error than the usual fourthorder schemes. The integral invariants of the shallowwater equations are calculated at each timestep and were determined to be well conserved during the numerical integration, ensuring that a realistic nonlinear structure is obtained. A SchumannWallington lowpass filtering procedure was incorporated in the program to overcome the increased aliasing due to the higher accuracy method. A thirdorder boundary condition is imposed, preserving the overall fourthorder convergence rate of the interior approximation. 
Homepage:  http://people.sc.fsu.edu/~inavon/pubs1/exshall4.pdf 
Keywords:  implicit compact fourthorder Fortran program; shallowwater equations; conservationlaw 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 fourthorder Fortran program for solving the shallowwater equations in conservationlaw form. Zbl 0473.76030 Navon, I. M.; Riphagen, H. A. 
1981

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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 (65XX) 
2  Partial differential equations (35XX) 
2  Fluid mechanics (76XX) 
1  Computer science (68XX) 
1  Operations research, mathematical programming (90XX) 