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An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations. (English) Zbl 0451.65055

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65Y99 Computer aspects of numerical algorithms
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[1] R. England, Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations, Comput. J. 12 (1969/1970), 166 – 170. · Zbl 0182.21903
[2] W. H. ENRIGHT, T. E. HULL & B. LINDBERG, ”Comparing numerical methods for stiff systems of o.d.e.:s,” BIT, v. 15, 1975, pp. 1-10. · Zbl 0301.65040
[3] C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. · Zbl 1145.65316
[4] S. P. NØRSETT, Semi-Explicit Runge-Kutta Methods, Technical Report 6, Dept. of Math., Univ. of Trondheim, 1974.
[5] Syvert P. Nørsett and Arne Wolfbrandt, Attainable order of rational approximations to the exponential function with only real poles, Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 2, 200 – 208. · Zbl 0361.41011
[6] A. WOLFBRANDT, A Study of Rosenbrock Processes with Respect to Order Conditions and Stiff Stability, Thesis, Chalmers Univ. of Technology, Goteborg, Sweden, 1977.
[7] Arne Wolfbrandt, A note on a recent result of rational approximations to the exponential function, Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 3, 367 – 368. · Zbl 0371.41007
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