van der Houwen, P. J.; Sommeijer, B. P. Euler-Chebyshev methods for integro-differential equations. (English) Zbl 0881.65141 Appl. Numer. Math. 24, No. 2-3, 203-218 (1997). Some explicit methods are constructed and analysed for solving initial value problems for systems of integro-differential equations with expensive right hand side functions whose Jacobian has its stiff eigenvalues along the negative axis. Reviewer: Hu Chuangan (Tianjin) Cited in 10 Documents MSC: 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 45J05 Integro-ordinary differential equations Keywords:Euler-Chebyshev methods; extended real stability boundaries; initial value problems; systems of integro-differential equations; stiff eigenvalues PDF BibTeX XML Cite \textit{P. J. van der Houwen} and \textit{B. P. Sommeijer}, Appl. Numer. Math. 24, No. 2--3, 203--218 (1997; Zbl 0881.65141) Full Text: DOI OpenURL References: [1] Bakker, M., Analytic aspects of a minimax problem, (Report TN 62 (1971), Mathematisch Centrum: Mathematisch Centrum Amsterdam), (in Dutch) [2] Brunner, H.; van der Houwen, P. J., The Numerical Solution of Volterra Equations, (CWI Monographs, 3 (1986), North-Holland: North-Holland Amsterdam) · Zbl 0611.65092 [3] Brunner, H.; Lambert, J. D., Stability of numerical methods for Volterra integro-differential equations, Computing, 12, 75-89 (1974) · Zbl 0282.65088 [4] Cushing, J. M., Integro-Differential Equations and Delay Models in Population Dynamics, (Lecture Notes in Biomathematics, 20 (1977), Springer: Springer Berlin) · Zbl 0363.92014 [5] Golub, G. H.; van Loan, C. F., Matrix Computations (1989), John Hopkins University Press: John Hopkins University Press London · Zbl 0733.65016 [6] Jameson, A., The evolution of computational methods in aerodynamics, J. Appl. Mech., 50, 1052-1076 (1983) · Zbl 0556.76045 [7] Lerat, A., A class of implicit difference schemes for hyperbolic conservation laws, C. R. Acad. Sci. Paris Sér. I Math., 288, 1033-1036 (1979), (in French) · Zbl 0439.65075 [8] Sommeijer, B. P.; van der Houwen, P. J., On the economization of stabilized Runge-Kutta methods with applications to parabolic initial value problems, Z. Angew. Math. Mech., 61, 105-114 (1981) · Zbl 0461.65056 [9] Turkel, E., Acceleration to a steady state for the Euler equations, (Numerical Methods for the Euler Equations of Fluid Dynamics (1985), SIAM: SIAM Philadelphia, PA), 218-311 [10] van der Houwen, P. J.; Boon, C.; Wubs, F. W., Analysis of smoothing matrices for the preconditioning of elliptic difference equations, Z. Angew. Math. Mech., 68, 3-10 (1988) · Zbl 0637.65101 [11] van der Houwen, P. J.; Sommeijer, B. P., On the internal stability of explicit, \(m\)-stage Runge-Kutta methods for large \(m\)-values, Z. Angew. Math. Mech., 60, 479-485 (1980) · Zbl 0455.65052 [12] van der Houwen, P. J.; Sommeijer, B. P., A special class of multistep Runge-Kutta methods with extended real stability interval, IMA J. Numer. Anal., 2, 183-209 (1982) · Zbl 0481.65038 [13] van der Houwen, P. J.; Sommeijer, B. P., Improving the stability of predictor-corrector methods by residue smoothing, IMA J. Numer. Anal., 10, 361-378 (1990) · Zbl 0704.65060 [14] Vasudeva Murthy, A. S.; Verwer, J. G., Solving parabolic integro-differential equations by an explicit integration method, J. Comput. Appl. Math., 39, 121-132 (1992) · Zbl 0746.65102 [15] Verwer, J. G.; Blom, J. G.; Hundsdorfer, W. H., An implicit-explicit approach for atmospheric transport-chemistry problems, Appl. Numer. Math., 20, 191-209 (1996) · Zbl 0853.76092 [16] Wilson, J. C., Stability of Richtmyer-type difference schemes in any finite number of space variables and their comparison with multistep Strang schemes, J. Inst. Math. Appl., 10, 238-257 (1972) · Zbl 0249.65063 [17] Wubs, F. W., Stabilization of explicit methods for hyperbolic partial differential equations, Internat. J. Numer. Methods Fluids, 6, 641-657 (1986) · Zbl 0611.65056 [18] Wubs, F. W., Numerical solution of the shallow-water equations, (Thesis (1987), University of Amsterdam) · Zbl 0653.76011 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.