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International Journal of Computer Mathematics Volume 29, 1989 - Issue 2-4
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Original Articles

Extended one-step methods for the numerical solution of ordinary differential equations

I. B. Jacques Department of Mathematics, Coventry Polytechnic, Priory Street, West Midlands, Coventry, UK
Pages 247-255 | Received 21 Jun 1988, Accepted 15 Jul 1988, Published online: 08 May 2007

Citations (21)

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Read on this site (7)

A. A. Salama & S. A. Bakr. (2004) Optimal extended one-step schemes of exponential type for stiff initial-value problems. International Journal of Computer Mathematics 81:11, pages 1363-1379.
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A.A. Salama. (2004) HIGHER-ORDER METHOD FOR SOLVING FREE BOUNDARY-VALUE PROBLEMS. Numerical Heat Transfer, Part B: Fundamentals 45:4, pages 385-394.
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H Bulut & M Inc. (2000) A two step method for the numerical integration of stiff differential equations. International Journal of Computer Mathematics 73:3, pages 333-340.
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T. Van Hecke, G. VandenG Berghe, M. Van Daele & H De Meyer. (1997) A variable-step variable-order algorithm for systems of stiff odes. International Journal of Computer Mathematics 63:1-2, pages 149-157.
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M.Van Daele, G.Vanden Berghe & H.De Meyer. (1996) A general theory of stabilized extended one-step methods for odes. International Journal of Computer Mathematics 60:3-4, pages 253-263.
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M. M. Chawla, M. A. Al-Zanaidi & M. S Al-Sahhar. (1994) Stabilized fourth order extended methods for the numerical solution of odes. International Journal of Computer Mathematics 52:1-2, pages 99-107.
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D.M. Kondrat & D.I.B. Jacques. (1992) Extended a-stable two-step methods for the numerical solution of ordinary differential equations. International Journal of Computer Mathematics 42:1-2, pages 117-124.
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Articles from other publishers (14)

F. Ibrahim, K. Hattaf, F. A. Rihan & S. Turek. (2016) Numerical method based on extended one-step schemes for optimal control problem with time-lags. International Journal of Dynamics and Control 5:4, pages 1172-1181.
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Higinio Ramos & Gurjinder Singh. (2017) A tenth order -stable two-step hybrid block method for solving initial value problems of ODEs . Applied Mathematics and Computation 310, pages 75-88.
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M. EL-KADY & M. BIOMY. (2011) INTERACTIVE CHEBYSHEV–LEGENDRE ALGORITHM FOR LINEAR QUADRATIC OPTIMAL REGULATOR SYSTEMS. International Journal of Wavelets, Multiresolution and Information Processing 09:03, pages 459-483.
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Mustafa Inc. (2007) New L-stable method for numerical solutions of ordinary differential equations. Applied Mathematics and Computation 188:1, pages 779-785.
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Mustafa Inc. (2007) An L-stable extended two-step method for the integration of ordinary differential equations. Applied Mathematics and Computation 186:2, pages 1395-1401.
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A.A. Salama. (2006) Numerical methods based on extended one-step methods for solving optimal control problems. Applied Mathematics and Computation 183:1, pages 243-250.
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M. Van Daele & G. Vanden Berghe. (2004) Extended One‐Step Methods: An Exponential Fitting Approach. Applied Numerical Analysis & Computational Mathematics 1:2, pages 353-362.
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M.M. Chawla, M.A. Al-Zanaidi & M.G. Al-Aslab. (2000) Extended one-step time-integration schemes for convection-diffusion equations. Computers & Mathematics with Applications 39:3-4, pages 71-84.
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M.M. Chawla & M.A. Al-Zanaidi. (1999) An extended trapezoidal formula for the diffusion equation. Computers & Mathematics with Applications 38:2, pages 51-59.
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H De Meyer, G Vanden Berghe, T Van Hecke & M Van Daele. (1997) On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods. Journal of Computational and Applied Mathematics 87:1, pages 147-167.
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H. De Meyer, T. Van Hecke, G.Vanden Berghe & M. Van Daele. (1996) Multistride L-Stable fourth-order methods for the numerical solution of ODEs. Computers & Mathematics with Applications 32:7, pages 1-8.
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M.M. Chawla, A.A. Karaballi & M.S. Al-Sahhar. (1996) Extended double-stride L-stable methods for the numerical solution of ODEs. Computers & Mathematics with Applications 31:2, pages 1-6.
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M.M. Chawla, M.A. Al-Zanaidi & M.S. Al-Sahhar. (1995) A class of stabilized extended one-step methods for the numerical solution of ODEs. Computers & Mathematics with Applications 29:10, pages 79-84.
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H. De Meyer, G. Vanden Berghe & J. Vanthournout. (1991) Modified backward differentiation methods of the Adams-type based on exponential interpolation. Computers & Mathematics with Applications 21:2-3, pages 171-179.
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