Ahmad, I.; Berzins, M. MOL solvers for hyperbolic PDEs with source terms. (English) Zbl 0986.65084 Math. Comput. Simul. 56, No. 2, 115-125 (2001). The authors consider the applications of the algorithm of the method of lines (MOL) to convection-reaction problems modelled by first order hyperbolic equations with stiff source terms (PDEs). Monotone spatial discretisation schemes with space/time error balancing, in which the advective terms are treated explicitly by applying the second-order limited discretisation, are used to reduce the PDEs to a system of ordinary differential equations (ODEs) in time. The backward Euler method and a Gauss-Seidel iteration for the source terms alone are applied to provide an efficient solver for the system of the ODEs. Numerical experiments are presented to illustrate the performance of the method. Reviewer: Song Jiang (Beijing) Cited in 6 Documents MSC: 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65H10 Numerical computation of solutions to systems of equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35Q35 PDEs in connection with fluid mechanics 65Y20 Complexity and performance of numerical algorithms Keywords:method of lines; conservation laws with stiff source terms; convection-reaction problems; Gauss-Seidel iteration; algorithm; first order hyperbolic equations; backward Euler method; numerical experiments; performance Software:nag PDFBibTeX XMLCite \textit{I. Ahmad} and \textit{M. Berzins}, Math. Comput. Simul. 56, No. 2, 115--125 (2001; Zbl 0986.65084) Full Text: DOI References: [1] I. Ahmad, The Numerical Solution of Reacting Flow Problems, Ph.D. Thesis, School of Computer Studies, University of Leeds, 1999.; I. Ahmad, The Numerical Solution of Reacting Flow Problems, Ph.D. Thesis, School of Computer Studies, University of Leeds, 1999. [2] Ahmad, I.; Berzins, M., An algorithm for ODEs from atmospheric dispersion problems, Appl. Num. Math., 25, 137-149 (1997) · Zbl 0889.65085 [3] Berzins, M., Temporal error control for convection-dominated equations in two space dimensions, SIAM J. Sci. Stat. Comput., 16, 558-580 (1995) · Zbl 0830.65090 [4] Berzins, M.; Ware, J. M., Solving convection and convection reaction problems using the MOL, Appl. Num. Math., 20, 83-99 (1996) · Zbl 0857.65095 [5] Donat, R.; Marquina, A., Capturing shock reflections: an improved flux formula, J. Comput. Phys., 125, 42-58 (1996) · Zbl 0847.76049 [6] R.P. Fedkiw, A Survey of Chemically Reacting, Compressible Flow, Ph.D. Dissertation, UCLA, 1966.; R.P. Fedkiw, A Survey of Chemically Reacting, Compressible Flow, Ph.D. Dissertation, UCLA, 1966. [7] Fedkiw, R. P.; Merriman, B.; Osher, S., High accuracy numerical methods for thermally perfect gas flows with chemistry, J. Comput. Phys., 132, 175-190 (1997) · Zbl 0888.76053 [8] Leveque, R. J.; Yee, H. C., A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys., 86, 187-210 (1990) · Zbl 0682.76053 [9] Papalexandris, M. V.; Leonard, A.; Dimotakis, P. E., Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension, J. Comput. Phys., 134, 31-61 (1997) · Zbl 0880.65074 [10] Pennington, S. V.; Berzins, M., New NAG library software for first-order partial differential equations, ACM Trans. Math. Software, 20, 63-99 (1994) · Zbl 0888.65109 [11] Tang, T., Convergence analysis for operator splitting method applied to conservation laws with stiff source terms, SIAM J. Num. Anal., 35, 5, 1939-1968 (1998) · Zbl 0921.35103 [12] Ton, V. T.; Karagozian, A. R.; Marble, F. E.; Osher, S. J.; Engquist, B. E., Numerical simulation of high speed chemically reacting flow, Theoret. Comput. Fluid Dynamics, 6, 161-179 (1994) · Zbl 0808.76062 [13] Verwer, J. G., Gauss-Seidel iteration for stiff odes from chemical kinetics, SIAM J. Sci. Comput., 15, 1243-1250 (1994) · Zbl 0804.65068 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.