1 write a subroutine or procedure to perform one step

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Unformatted text preview: ods for sti o.d.e.'s. SIAM J. Numer. Anal., 14:1006{1021, 1977. 3] U.M. Ascher and L.R. Petzold. Computer Methods for Ordinary Di erential Equations and Di erential-Algebraic Equations. SIAM, Philadelphia, 1998. 4] R.L. Burden and J.D. Faires. Numerical Analysis. PWS-Kent, Boston, fth edition, 1993. 5] K. Burrage. A special family of runge-kutta methods for solving sti di erential equations. BIT, 18:22 { 41, 1978. 6] K. Burrage, J.C. Butcher, and R.H. Chipman. An implementation of singly-implicit runge-kutta methods. BIT, 20:326 { 340, 1980. 7] J.C. Butcher. Implicit runge-kutta processes. Maths. Comp., 18:50{64, 1964. 8] J.C. Butcher. On the attainable order of runge-kutta methods. Maths. Comp., 19:408 { 417, 1965. 9] J.C. Butcher. On the implementation of implicit runge-kutta methods. BIT, 16:237 { 240, 1976. 10] J.C. Butcher. A transformed implicit runge-kutta method. J. Assoc. Comput. Mach., 26:731 { 738, 1979. 57 11] J.C. Butcher. The Numerical Analysis of Ordinary Di erential Equ...
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