Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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HIGH ORDER IMPLICIT METHOD FOR ODES STIFF SYSTEMS

  • Published : 2001.01.01

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Abstract

This paper presents a new difference scheme for numerical solution of stiff system of ODE’s. The present study is mainly motivated to develop an absolutely stable numerical method with a high order of approximation. In this work a double implicit A-stable difference scheme with the sixth order of approximation is suggested. Another purpose of this study is to introduce automatic choice of the integration step size of the difference scheme which is derived from the proposed scheme and the one step scheme of the fourth order of approximation. The algorithm was tested by means of solving the Kreiss problem and a chemical kinetics problem. The behavior of the gas explosive mixture (H₂+ O₂) in a closed space with a mobile piston is considered in test problem 2. It is our conclusion that a hydrogen-operated engine will permit to decrease the emitted levels of hazardous atmospheric pollutants.

Keywords

References

  1. SIAM J. Numer. Anal. no.21 ODE methods for the solution of differential/algebraic systems C.W.Gear;L.R.Petzold
  2. BIT no.3 A Special Stability Problem for Linear Multistep Methods G.Dahlquist
  3. Numerical Analysis, Dundee 1975, Lecture Notes in Mathematics v.506 Error analysis of a class of methods for stiff non-linear initial value problems G.Dahlquist
  4. Computing Methods in Applied Science and Engineering Some problems related to the stiff non-linear differential systems G.Dahlquist;G.Soderlind;V.R.Glowinski(ed.);J.L.Lions(ed.)
  5. Stability of Runge-Kutta methods for stiff nonlinear differential equations K.Dekker;J.G.Verwer
  6. Solving ordinary differential equations.Ⅱ.Stiff and differential algebraic problems E.Hairer;G.Wanner
  7. Matematicheskoe modelirovanie v.7 no.5 Numerical methods of solving stiff systems N.N.Kalitkin
  8. SIAM J. Numer. Anal. no.15 Difference methods for stiff ordinary differential equations H.O.Kreiss
  9. Numerical methods of solving stiff systems Yu.V.Rakitskyi;S.M.Ustinov;I.G.Chernorutskyi
  10. Comp.J. v.5 no.4 Some general implicit processes for the numerical solution of differential equations H.H.Rosenbrock
  11. Numerical Analysis A.A.Samarskyi;A.V.Gulin
  12. Izvestiya AN SSSR, Mekh. Zhidk. i Gaza no.4 Sphere with supersonic flow of explosive mixture V.P.Stulov
  13. Abstracts of Intern. Congress of Mathematics, Berlin Twice implicit scheme with accuracy control and its application to the chemical kinetics problems Tatiana Vasilyeva
  14. Abstracts of Intern. conf. "Mathematics. Computer. Education" Moscow-Pushchino Application of the new implicit scheme to the solution of chemical kinetics problem T.A.Vasilyeva;E.I.Vasilyev